Abstract Let G be a simple connected graph of order n and size m. The matrix L(G)= D(G)− A(G) is called the Laplacian matrix of the graph G,where D(G) and A(G) are the degree diagonal matrix and the adjacency matrix, respectively. Let the vertex degree sequence be d1 ≥ d2 ≥··· ≥ dn and let μ1 ≥ μ2 ≥··· ≥ μn−1 >μn = 0 be the eigenvalues of the Laplacian matrix of G. The graph invariants, Laplacian energy (LE), the Laplacian-energy-like invariant (LEL) and the Kirchhoff index (Kf), are defined in terms of the Laplacian eigenvalues of graph G, as LE=∑i=1n| μi-2mn | LE = sumnolimits_{i = 1}^n {left| {{mu _i} - {{2m} over n}} right|} , LEL=∑i=1n-1μi LEL = sumnolimits_{i = 1}^{n - 1} {sqrt {{mu _i}} } and Kf=n∑i=1n-11μi Kf = nsumnolimits_{i = 1}^{n - 1} {{1 over {{mu _i}}}} respectively. In this paper, we obtain a new bound for the Laplacian-energy-like invariant LEL and establish the relations between Laplacian-energy-like invariant LEL and the Kirchhoff index Kf.Further,weobtain the relations between the Laplacian energy LE and Kirchhoff index Kf.
{"title":"Computing Laplacian energy, Laplacian-energy-like invariant and Kirchhoff index of graphs","authors":"S. Bhatnagar, Merajuddin, S. Pirzada","doi":"10.2478/ausi-2022-0011","DOIUrl":"https://doi.org/10.2478/ausi-2022-0011","url":null,"abstract":"Abstract Let G be a simple connected graph of order n and size m. The matrix L(G)= D(G)− A(G) is called the Laplacian matrix of the graph G,where D(G) and A(G) are the degree diagonal matrix and the adjacency matrix, respectively. Let the vertex degree sequence be d1 ≥ d2 ≥··· ≥ dn and let μ1 ≥ μ2 ≥··· ≥ μn−1 >μn = 0 be the eigenvalues of the Laplacian matrix of G. The graph invariants, Laplacian energy (LE), the Laplacian-energy-like invariant (LEL) and the Kirchhoff index (Kf), are defined in terms of the Laplacian eigenvalues of graph G, as LE=∑i=1n| μi-2mn | LE = sumnolimits_{i = 1}^n {left| {{mu _i} - {{2m} over n}} right|} , LEL=∑i=1n-1μi LEL = sumnolimits_{i = 1}^{n - 1} {sqrt {{mu _i}} } and Kf=n∑i=1n-11μi Kf = nsumnolimits_{i = 1}^{n - 1} {{1 over {{mu _i}}}} respectively. In this paper, we obtain a new bound for the Laplacian-energy-like invariant LEL and establish the relations between Laplacian-energy-like invariant LEL and the Kirchhoff index Kf.Further,weobtain the relations between the Laplacian energy LE and Kirchhoff index Kf.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"49 1","pages":"185 - 198"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83661878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Niranjana Sudheer, Ann Cherian George, Achu Aniyan, S. Naduvath
Abstract A signed graph is a graph in which positive or negative signs are assigned to its edges. We consider equitable colouring and Hamiltonian colouring to obtain induced signed graphs. An equitable colour-induced signed graph is a signed graph constructed from a given graph in which each edge uv receives a sign (−1)|c(v)−c(u)|,where c is an equitable colouring of vertex v. A Hamiltonian colour-induced signed graph is a signed graph obtained from a graph G in which for each edge e = uv, the signature function σ(uv)=(−1)|c(v)−c(u)|, gives a sign such that, |c(u)− c(v)| ≥ n − 1 − D(u, v) where c is a function that assigns a colour to each vertex satisfying the given condition. This paper discusses the properties and characteristics of signed graphs induced by the equitable and Hamiltonian colouring of graphs.
带符号图是指在图的边上有正号或负号的图。我们考虑了公平着色和哈密顿着色来得到诱导符号图。签署公平colour-induced图是一个签名图由一个给定的图中每条边uv接收信号(−1)| (v)−c (u) |,其中c是一个公平的顶点v哈密顿colour-induced签名图的着色是一个签名图获得从一个图G的每个边e =紫外线,签名函数σ(紫外线)=(−1)| (v)−c (u) |,给了一个信号,| c (u)−c (v) |≥n−−1 D (u, v), c是一个函数,分配一个颜色每个顶点满足给定的条件。讨论了由图的公平着色和哈密顿着色所导出的符号图的性质和特征。
{"title":"Some new results on colour-induced signed graphs","authors":"Niranjana Sudheer, Ann Cherian George, Achu Aniyan, S. Naduvath","doi":"10.2478/ausi-2022-0019","DOIUrl":"https://doi.org/10.2478/ausi-2022-0019","url":null,"abstract":"Abstract A signed graph is a graph in which positive or negative signs are assigned to its edges. We consider equitable colouring and Hamiltonian colouring to obtain induced signed graphs. An equitable colour-induced signed graph is a signed graph constructed from a given graph in which each edge uv receives a sign (−1)|c(v)−c(u)|,where c is an equitable colouring of vertex v. A Hamiltonian colour-induced signed graph is a signed graph obtained from a graph G in which for each edge e = uv, the signature function σ(uv)=(−1)|c(v)−c(u)|, gives a sign such that, |c(u)− c(v)| ≥ n − 1 − D(u, v) where c is a function that assigns a colour to each vertex satisfying the given condition. This paper discusses the properties and characteristics of signed graphs induced by the equitable and Hamiltonian colouring of graphs.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"1 1","pages":"338 - 353"},"PeriodicalIF":0.3,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90114532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The transmission of a vertex u in a connected graph G is defined as σ(u) = Σv∈V(G) d(u, v) and reciprocal transmission of a vertex u is defined as rs(u)=∑v∈V(G)1d(u,v) rs(u) = sumnolimits_{v in Vleft( G right)} {{1 over {dleft( {u,v} right)}}} , where d(u, v) is the distance between vertex u and v in G. In this paper we define new distance based topological index of a connected graph G called transmission-reciprocal transmission index TRT(G)=∑uv∈E(G)(σ(u)rs(u)+σ(v)rs(v)) TRTleft( G right) = sumnolimits_{uv in Eleft( G right)} {left( {{{sigma left( u right)} over {rsleft( u right)}} + {{sigma left( v right)} over {rsleft( v right)}}} right)} and its coindex TRT¯(G)=∑uv∉E(G)(σ(u)rs(u)+σ(v)rs(v)) overline {TRT} left( G right) = sumnolimits_{uv notin Eleft( G right)} {left( {{{sigma left( u right)} over {rsleft( u right)}} + {{sigma left( v right)} over {rsleft( v right)}}} right)} , where E(G) is the edge set of a graph G and establish the relation between TRT(G) and TRT¯(G) overline {TRT} left( G right) (G). Further compute this index for some standard class of graphs and obtain bounds for it.
{"title":"Transmission-reciprocal transmission index and coindex of graphs","authors":"H. Ramane, Deepa V. Kitturmath, Kavita Bhajantri","doi":"10.2478/ausi-2022-0006","DOIUrl":"https://doi.org/10.2478/ausi-2022-0006","url":null,"abstract":"Abstract The transmission of a vertex u in a connected graph G is defined as σ(u) = Σv∈V(G) d(u, v) and reciprocal transmission of a vertex u is defined as rs(u)=∑v∈V(G)1d(u,v) rs(u) = sumnolimits_{v in Vleft( G right)} {{1 over {dleft( {u,v} right)}}} , where d(u, v) is the distance between vertex u and v in G. In this paper we define new distance based topological index of a connected graph G called transmission-reciprocal transmission index TRT(G)=∑uv∈E(G)(σ(u)rs(u)+σ(v)rs(v)) TRTleft( G right) = sumnolimits_{uv in Eleft( G right)} {left( {{{sigma left( u right)} over {rsleft( u right)}} + {{sigma left( v right)} over {rsleft( v right)}}} right)} and its coindex TRT¯(G)=∑uv∉E(G)(σ(u)rs(u)+σ(v)rs(v)) overline {TRT} left( G right) = sumnolimits_{uv notin Eleft( G right)} {left( {{{sigma left( u right)} over {rsleft( u right)}} + {{sigma left( v right)} over {rsleft( v right)}}} right)} , where E(G) is the edge set of a graph G and establish the relation between TRT(G) and TRT¯(G) overline {TRT} left( G right) (G). Further compute this index for some standard class of graphs and obtain bounds for it.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"8 1","pages":"84 - 103"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87100230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L2 and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.
{"title":"Limit laws for two distance-based indices in random recursive tree models","authors":"S. Naderi, R. Kazemi, M. Behzadi","doi":"10.2478/ausi-2022-0003","DOIUrl":"https://doi.org/10.2478/ausi-2022-0003","url":null,"abstract":"Abstract In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L2 and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"1 1","pages":"35 - 48"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90236970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The concept of first KCD signless Laplacian energy is initiated in this article. Moreover, we determine first KCD signless Laplacian spectrum and first KCD signless Laplacian energy for some class of graphs and their complement.
{"title":"Signless Laplacian energy of a first KCD matrix","authors":"K. G. Mirajkar, A. Morajkar","doi":"10.2478/ausi-2022-0002","DOIUrl":"https://doi.org/10.2478/ausi-2022-0002","url":null,"abstract":"Abstract The concept of first KCD signless Laplacian energy is initiated in this article. Moreover, we determine first KCD signless Laplacian spectrum and first KCD signless Laplacian energy for some class of graphs and their complement.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"76 1","pages":"22 - 34"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83191156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The problem of varying length recordings is a well-known issue in paralinguistics. We investigated how to resolve this problem using the bag-of-audio-words feature extraction approach. The steps of this technique involve preprocessing, clustering, quantization and normalization. The bag-of-audio-words technique is competitive in the area of speech emotion recognition, but the method has several parameters that need to be precisely tuned for good efficiency. The main aim of our study was to analyse the effectiveness of bag-of-audio-words method and try to find the best parameter values for emotion recognition. We optimized the parameters one-by-one, but built on the results of each other. We performed the feature extraction, using openSMILE. Next we transformed our features into same-sized vectors with openXBOW, and finally trained and evaluated SVM models with 10-fold-crossvalidation and UAR. In our experiments, we worked with a Hungarian emotion database. According to our results, the emotion classification performance improves with the bag-of-audio-words feature representation. Not all the BoAW parameters have the optimal settings but later we can make clear recommendations on how to set bag-of-audio-words parameters for emotion detection tasks.
{"title":"Using the Bag-of-Audio-Words approach for emotion recognition","authors":"Mercedes Vetráb, G. Gosztolya","doi":"10.2478/ausi-2022-0001","DOIUrl":"https://doi.org/10.2478/ausi-2022-0001","url":null,"abstract":"Abstract The problem of varying length recordings is a well-known issue in paralinguistics. We investigated how to resolve this problem using the bag-of-audio-words feature extraction approach. The steps of this technique involve preprocessing, clustering, quantization and normalization. The bag-of-audio-words technique is competitive in the area of speech emotion recognition, but the method has several parameters that need to be precisely tuned for good efficiency. The main aim of our study was to analyse the effectiveness of bag-of-audio-words method and try to find the best parameter values for emotion recognition. We optimized the parameters one-by-one, but built on the results of each other. We performed the feature extraction, using openSMILE. Next we transformed our features into same-sized vectors with openXBOW, and finally trained and evaluated SVM models with 10-fold-crossvalidation and UAR. In our experiments, we worked with a Hungarian emotion database. According to our results, the emotion classification performance improves with the bag-of-audio-words feature representation. Not all the BoAW parameters have the optimal settings but later we can make clear recommendations on how to set bag-of-audio-words parameters for emotion detection tasks.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"1 1","pages":"1 - 21"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83600793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Suppose that the zero-divisor graph of a commutative semi-group S, be a complete graph with an end vertex. In this paper, we determine the structure of the annihilator graph S and we show that if Z(S)= S, then the annihilator graph S is a disconnected graph.
{"title":"Annihilator graphs of a commutative semigroup whose Zero-divisor graphs are a complete graph with an end vertex","authors":"Seyed Mohammad Sakhdari, M. Afkhami","doi":"10.2478/ausi-2022-0008","DOIUrl":"https://doi.org/10.2478/ausi-2022-0008","url":null,"abstract":"Abstract Suppose that the zero-divisor graph of a commutative semi-group S, be a complete graph with an end vertex. In this paper, we determine the structure of the annihilator graph S and we show that if Z(S)= S, then the annihilator graph S is a disconnected graph.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"1 1","pages":"119 - 136"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91042708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we propose to create an end-to-end brain tumor segmentation system that applies three variants of the well-known U-Net convolutional neural networks. In our results we obtain and analyse the detection performances of U-Net, VGG16-UNet and ResNet-UNet on the BraTS2020 training dataset. Further, we inspect the behavior of the ensemble model obtained as the weighted response of the three CNN models. We introduce essential preprocessing and post-processing steps so as to improve the detection performances. The original images were corrected and the different intensity ranges were transformed into the 8-bit grayscale domain to uniformize the tissue intensities, while preserving the original histogram shapes. For post-processing we apply region connectedness onto the whole tumor and conversion of background pixels into necrosis inside the whole tumor. As a result, we present the Dice scores of our system obtained for WT (whole tumor), TC (tumor core) and ET (enhanced tumor) on the BraTS2020 training dataset.
{"title":"U-Net architecture variants for brain tumor segmentation of histogram corrected images","authors":"Szidónia Lefkovits, László Lefkovits","doi":"10.2478/ausi-2022-0004","DOIUrl":"https://doi.org/10.2478/ausi-2022-0004","url":null,"abstract":"Abstract In this paper we propose to create an end-to-end brain tumor segmentation system that applies three variants of the well-known U-Net convolutional neural networks. In our results we obtain and analyse the detection performances of U-Net, VGG16-UNet and ResNet-UNet on the BraTS2020 training dataset. Further, we inspect the behavior of the ensemble model obtained as the weighted response of the three CNN models. We introduce essential preprocessing and post-processing steps so as to improve the detection performances. The original images were corrected and the different intensity ranges were transformed into the 8-bit grayscale domain to uniformize the tissue intensities, while preserving the original histogram shapes. For post-processing we apply region connectedness onto the whole tumor and conversion of background pixels into necrosis inside the whole tumor. As a result, we present the Dice scores of our system obtained for WT (whole tumor), TC (tumor core) and ET (enhanced tumor) on the BraTS2020 training dataset.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"25 1","pages":"49 - 74"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73902668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract For a commutative ring R with identity 1, the zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is the set of non-zero zero divisors Z*(R) and the two vertices x and y ∈ Z*(R) are adjacent if and only if xy = 0. In this paper, we compute the values of some graph parameters of the zero-divisor graph associated to the ring of Gaussian integers modulo n, ℤn[i] and the ring of integers modulo n, ℤn.
{"title":"On graphs associated to ring of Guassian integers and ring of integers modulo n","authors":"S. Pirzada, M. Bhat","doi":"10.2478/ausi-2022-0005","DOIUrl":"https://doi.org/10.2478/ausi-2022-0005","url":null,"abstract":"Abstract For a commutative ring R with identity 1, the zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is the set of non-zero zero divisors Z*(R) and the two vertices x and y ∈ Z*(R) are adjacent if and only if xy = 0. In this paper, we compute the values of some graph parameters of the zero-divisor graph associated to the ring of Gaussian integers modulo n, ℤn[i] and the ring of integers modulo n, ℤn.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"24 1","pages":"75 - 83"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74549877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work, the Seidel Laplacian spectrum of graphs are determined. Then new bounds are presented for the Seidel Laplacian energy of regular graphs and graphs by using their Seidel Laplacian spectrum and other techniques. Further, the Seidel Laplacian energy of specific graphs are computed.
{"title":"On Seidel Laplacian matrix and energy of graphs","authors":"N. Yalçın","doi":"10.2478/ausi-2022-0007","DOIUrl":"https://doi.org/10.2478/ausi-2022-0007","url":null,"abstract":"Abstract In this work, the Seidel Laplacian spectrum of graphs are determined. Then new bounds are presented for the Seidel Laplacian energy of regular graphs and graphs by using their Seidel Laplacian spectrum and other techniques. Further, the Seidel Laplacian energy of specific graphs are computed.","PeriodicalId":41480,"journal":{"name":"Acta Universitatis Sapientiae Informatica","volume":"3 1","pages":"104 - 118"},"PeriodicalIF":0.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89588571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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