Pub Date : 2022-05-10DOI: 10.1080/09728600.2022.2072789
A. Lourdusamy, I. Dhivviyanandam, S. K. Iammal
{"title":"Monophonic pebbling number and t-pebbling number of some graphs","authors":"A. Lourdusamy, I. Dhivviyanandam, S. K. Iammal","doi":"10.1080/09728600.2022.2072789","DOIUrl":"https://doi.org/10.1080/09728600.2022.2072789","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"28 1","pages":"108-111"},"PeriodicalIF":1.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77656160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-10DOI: 10.1080/09728600.2022.2070718
Payal, Sangita Kansal
{"title":"Structural matrices for Signed Petri net","authors":"Payal, Sangita Kansal","doi":"10.1080/09728600.2022.2070718","DOIUrl":"https://doi.org/10.1080/09728600.2022.2070718","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"455 1","pages":"102-107"},"PeriodicalIF":1.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81635050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-03DOI: 10.1080/09728600.2023.2236172
Iswar Mahato, M. Kannan
Let $T$ be a tree on $n$ vertices whose edge weights are positive definite matrices of order $s$. The squared distance matrix of $T$, denoted by $Delta$, is the $ns times ns$ block matrix with $Delta_{ij}=d(i,j)^2$, where $d(i,j)$ is the sum of the weights of the edges in the unique $(i,j)$-path. In this article, we obtain a formula for the determinant of $Delta$ and find ${Delta}^{-1}$ under some conditions.
{"title":"Squared distance matrices of trees with matrix weights","authors":"Iswar Mahato, M. Kannan","doi":"10.1080/09728600.2023.2236172","DOIUrl":"https://doi.org/10.1080/09728600.2023.2236172","url":null,"abstract":"Let $T$ be a tree on $n$ vertices whose edge weights are positive definite matrices of order $s$. The squared distance matrix of $T$, denoted by $Delta$, is the $ns times ns$ block matrix with $Delta_{ij}=d(i,j)^2$, where $d(i,j)$ is the sum of the weights of the edges in the unique $(i,j)$-path. In this article, we obtain a formula for the determinant of $Delta$ and find ${Delta}^{-1}$ under some conditions.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41435183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-03DOI: 10.1080/09728600.2022.2066490
Supachoke Isariyapalakul, Witsarut Pho-on, V. Khemmani
{"title":"Bounds on the connected local dimension of graphs in terms of the marked dimension and the clique number","authors":"Supachoke Isariyapalakul, Witsarut Pho-on, V. Khemmani","doi":"10.1080/09728600.2022.2066490","DOIUrl":"https://doi.org/10.1080/09728600.2022.2066490","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"55 1","pages":"95-101"},"PeriodicalIF":1.0,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84818962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-17DOI: 10.1080/09728600.2023.2219335
Saleem Khan, S. Pirzada
Let $G$ be a connected simple graph with $n$ vertices. The distance Laplacian matrix $D^{L}(G)$ is defined as $D^L(G)=Diag(Tr)-D(G)$, where $Diag(Tr)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the distance matrix of $G$. The eigenvalues of $D^{L}(G)$ are the distance Laplacian eigenvalues of $G$ and are denoted by $partial_{1}^{L}(G)geq partial_{2}^{L}(G)geq dots geq partial_{n}^{L}(G)$. The largest eigenvalue $partial_{1}^{L}(G)$ is called the distance Laplacian spectral radius. Lu et al. (2017), Fernandes et al. (2018) and Ma et al. (2018) completely characterized the graphs having some distance Laplacian eigenvalue of multiplicity $n-3$. In this paper, we characterize the graphs having distance Laplacian spectral radius of multiplicity $n-4$ together with one of the distance Laplacian eigenvalue as $n$ of multiplicity either 3 or 2. Further, we completely determine the graphs for which the distance Laplacian eigenvalue $n$ is of multiplicity $n-4$.
设$G$是一个有$n$个顶点的连通简单图。距离拉普拉斯矩阵$D^{L}（G）$定义为$D^L（G）=Diag（Tr）-D（G）美元，其中$Diag（Tr$）是顶点传输的对角矩阵，$D（G）是$G$的距离矩阵。$D^{L}（G）$的特征值是$G$的距离拉普拉斯特征值，表示为$partial_{1}^{L｝（G）geqpartial_。最大特征值$partial_{1}^{L}（G）$称为距离拉普拉斯谱半径。Lu et al.（2017），Fernandes et al.（2018）和Ma等人（2018）完全刻画了具有多重数$n-3$的距离拉普拉斯特征值的图。在本文中，我们将具有多重数$n-4$的距离拉普拉斯谱半径的图与距离拉普拉斯特征值之一一起刻画为多重数为3或2的$n$。此外，我们完全确定距离拉普拉斯特征值$n$为多重数$n-4$的图。
{"title":"On graphs with distance Laplacian eigenvalues of multiplicity n−4","authors":"Saleem Khan, S. Pirzada","doi":"10.1080/09728600.2023.2219335","DOIUrl":"https://doi.org/10.1080/09728600.2023.2219335","url":null,"abstract":"Let $G$ be a connected simple graph with $n$ vertices. The distance Laplacian matrix $D^{L}(G)$ is defined as $D^L(G)=Diag(Tr)-D(G)$, where $Diag(Tr)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the distance matrix of $G$. The eigenvalues of $D^{L}(G)$ are the distance Laplacian eigenvalues of $G$ and are denoted by $partial_{1}^{L}(G)geq partial_{2}^{L}(G)geq dots geq partial_{n}^{L}(G)$. The largest eigenvalue $partial_{1}^{L}(G)$ is called the distance Laplacian spectral radius. Lu et al. (2017), Fernandes et al. (2018) and Ma et al. (2018) completely characterized the graphs having some distance Laplacian eigenvalue of multiplicity $n-3$. In this paper, we characterize the graphs having distance Laplacian spectral radius of multiplicity $n-4$ together with one of the distance Laplacian eigenvalue as $n$ of multiplicity either 3 or 2. Further, we completely determine the graphs for which the distance Laplacian eigenvalue $n$ is of multiplicity $n-4$.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47903747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1080/09728600.2022.2111241
Praveen Mathil, Barkha Baloda, J. Kumar
Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted by $Gamma'(R)$, is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x notin Ry$ and $y notin Rx$. In this paper, first we study the Laplacian spectrum of $Gamma'(mathbb{Z}_n)$. We show that the graph $Gamma'(mathbb{Z}_{pq})$ is Laplacian integral. Further, we obtain the Laplacian spectrum of $Gamma'(mathbb{Z}_n)$ for $n = p^{n_1}q^{n_2}$, where $n_1, n_2 in mathbb{N}$ and $p, q$ are distinct primes. In order to study the Laplacian spectral radius and algebraic connectivity of $Gamma'(mathbb{Z}_n)$, we characterized the values of $n$ for which the Laplacian spectral radius is equal to the order of $Gamma'(mathbb{Z}_n)$. Moreover, the values of $n$ for which the algebraic connectivity and vertex connectivity of $Gamma'(mathbb{Z}_n)$ coincide are also described. At the final part of this paper, we obtain the Wiener index of $Gamma'(mathbb{Z}_n)$ for arbitrary $n$.
{"title":"On the cozero-divisor graphs associated to rings","authors":"Praveen Mathil, Barkha Baloda, J. Kumar","doi":"10.1080/09728600.2022.2111241","DOIUrl":"https://doi.org/10.1080/09728600.2022.2111241","url":null,"abstract":"Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denoted by $Gamma'(R)$, is an undirected simple graph whose vertices are the set of all non-zero and non-unit elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $x notin Ry$ and $y notin Rx$. In this paper, first we study the Laplacian spectrum of $Gamma'(mathbb{Z}_n)$. We show that the graph $Gamma'(mathbb{Z}_{pq})$ is Laplacian integral. Further, we obtain the Laplacian spectrum of $Gamma'(mathbb{Z}_n)$ for $n = p^{n_1}q^{n_2}$, where $n_1, n_2 in mathbb{N}$ and $p, q$ are distinct primes. In order to study the Laplacian spectral radius and algebraic connectivity of $Gamma'(mathbb{Z}_n)$, we characterized the values of $n$ for which the Laplacian spectral radius is equal to the order of $Gamma'(mathbb{Z}_n)$. Moreover, the values of $n$ for which the algebraic connectivity and vertex connectivity of $Gamma'(mathbb{Z}_n)$ coincide are also described. At the final part of this paper, we obtain the Wiener index of $Gamma'(mathbb{Z}_n)$ for arbitrary $n$.","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"1 1","pages":"238-248"},"PeriodicalIF":1.0,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74857659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-02DOI: 10.1080/09728600.2022.2057826
Yongsheng Rao, S. Kosari, Hao Guan, Maryam Akhoundi, S. Omidi
{"title":"A short note on the left A-Γ-hyperideals in ordered Γ-semihypergroups","authors":"Yongsheng Rao, S. Kosari, Hao Guan, Maryam Akhoundi, S. Omidi","doi":"10.1080/09728600.2022.2057826","DOIUrl":"https://doi.org/10.1080/09728600.2022.2057826","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"89 1","pages":"49-53"},"PeriodicalIF":1.0,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83546040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-02DOI: 10.1080/09728600.2022.2041365
A. Chin, H. Maimani, M. R. Pournaki, M. Sivagami, T. T. Chelvam
{"title":"Unitary Cayley graphs whose Roman domination numbers are at most four","authors":"A. Chin, H. Maimani, M. R. Pournaki, M. Sivagami, T. T. Chelvam","doi":"10.1080/09728600.2022.2041365","DOIUrl":"https://doi.org/10.1080/09728600.2022.2041365","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"35 1","pages":"36-40"},"PeriodicalIF":1.0,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84562333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-02DOI: 10.1080/09728600.2022.2058437
N. Rehman, M. Nazim, K. Selvakumar
{"title":"On the planarity, genus and crosscap of new extension of zero-divisor graph of commutative rings","authors":"N. Rehman, M. Nazim, K. Selvakumar","doi":"10.1080/09728600.2022.2058437","DOIUrl":"https://doi.org/10.1080/09728600.2022.2058437","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"10 8 1","pages":"61-68"},"PeriodicalIF":1.0,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86158058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-02DOI: 10.1080/09728600.2022.2057259
S. Ramachandran
{"title":"A property of most of the known non-reconstructible digraphs","authors":"S. Ramachandran","doi":"10.1080/09728600.2022.2057259","DOIUrl":"https://doi.org/10.1080/09728600.2022.2057259","url":null,"abstract":"","PeriodicalId":48497,"journal":{"name":"AKCE International Journal of Graphs and Combinatorics","volume":"31 1","pages":"41-48"},"PeriodicalIF":1.0,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73079815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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