Pub Date : 2023-07-25DOI: 10.9734/arjom/2023/v19i10720
Isagani S. Cabahug Jr.
For a connected nontrivial graph G, the maximum linear forest of G is the linear forest having maximum number of edges. The number of edges in a maximum linear forest is denoted by (ell)`(G). In this paper we determine the maximum linear forest of the join and union of nontrivial connected graphs G and H , denoted by G + H and G (cup) H , respectively.
{"title":"Maximum Linear Forest of Graphs Resulting from Some Binary Operations","authors":"Isagani S. Cabahug Jr.","doi":"10.9734/arjom/2023/v19i10720","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i10720","url":null,"abstract":"For a connected nontrivial graph G, the maximum linear forest of G is the linear forest having maximum number of edges. The number of edges in a maximum linear forest is denoted by (ell)`(G). In this paper we determine the maximum linear forest of the join and union of nontrivial connected graphs G and H , denoted by G + H and G (cup) H , respectively.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129836825","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}
Pub Date : 2023-07-22DOI: 10.9734/arjom/2023/v19i9717
John Mark R. Liwat, R. G. Eballe
{"title":"Pointwise Clique-Safe Domination in Graphs","authors":"John Mark R. Liwat, R. G. Eballe","doi":"10.9734/arjom/2023/v19i9717","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9717","url":null,"abstract":"<jats:p />","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132857406","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}
Pub Date : 2023-07-22DOI: 10.9734/arjom/2023/v19i9716
N. P. Akpan, N. Bassey
{"title":"Maintainability Modelling of Total Power Outage Data","authors":"N. P. Akpan, N. Bassey","doi":"10.9734/arjom/2023/v19i9716","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9716","url":null,"abstract":"<jats:p />","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129069541","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9710
I. S. Jr.
For any graphs G of order n, the spanning tree packing number, denoted by, of a graph G is the maximum number of edge disjoint spanning tree contained in G. In this study determine the spanning packing number of lexicographic product of graphs resulting from two path graphs.
{"title":"Spanning Tree Packing of Lexicographic Product of Graphs Resulting from Path and Complete Graphs","authors":"I. S. Jr.","doi":"10.9734/arjom/2023/v19i9710","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9710","url":null,"abstract":"For any graphs G of order n, the spanning tree packing number, denoted by, of a graph G is the maximum number of edge disjoint spanning tree contained in G. In this study determine the spanning packing number of lexicographic product of graphs resulting from two path graphs.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114713448","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9715
R. Tejaskumar, A. Ismayil
For a graph G = (V, E) of order K2 the minimum superior eccentric dominating energy SEed(G) is the sum of the eigen values obtained from the minimum superior eccentric dominating K x K matrix Ased (G) = (Seij) In this paper SEed(G) of standard graphs are computed. Properties, upper and lower bounds for SEed(G) are established.
对于K2阶图G = (V, E)，最小优偏心控制能SEed(G)是由最小优偏心控制K x K矩阵Ased (G) = (Seij)得到的特征值的和，本文计算了标准图的SEed(G)。建立了SEed(G)的性质、上界和下界。
{"title":"The Minimum Superior Eccentric Dominating Energy of Graphs","authors":"R. Tejaskumar, A. Ismayil","doi":"10.9734/arjom/2023/v19i9715","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9715","url":null,"abstract":"For a graph G = (V, E) of order K2 the minimum superior eccentric dominating energy SEed(G) is the sum of the eigen values obtained from the minimum superior eccentric dominating K x K matrix Ased (G) = (Seij) In this paper SEed(G) of standard graphs are computed. Properties, upper and lower bounds for SEed(G) are established.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117106762","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9712
I. S. Jr.
{"title":"On the 2-Rainbow Domination Number Over the γ-set of Some Classes of Graphs","authors":"I. S. Jr.","doi":"10.9734/arjom/2023/v19i9712","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9712","url":null,"abstract":"<jats:p />","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133826585","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9714
I. S. Jr.
For any graph G, the spanning tree packing number of (sigma) (G), is the maximum number of edge-disjoint spanning trees contained in G. In this study, we determined the maximum number of edge-disjoint spanning trees of the generalized petersen graph and cocktail graph.
{"title":"On Spanning Tree Packing Number of the Complement of Generalized Petersen Graph and Cocktail Party Graph","authors":"I. S. Jr.","doi":"10.9734/arjom/2023/v19i9714","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9714","url":null,"abstract":"For any graph G, the spanning tree packing number of (sigma) (G), is the maximum number of edge-disjoint spanning trees contained in G. In this study, we determined the maximum number of edge-disjoint spanning trees of the generalized petersen graph and cocktail graph.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133945120","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9713
K. Maheshwaran, R. J. Hussain, Nesrin Manav Tatar
This paper, we extends the new concept of common fixed point theorems in C*-algebra valued b-metric space (AV BMS) via ((mathfrak{F}); (phi)) - contractive mappings. Investigated are the common fixed points criteria for existence and uniqueness. Additionally, provide an illustrate an example.
{"title":"Common Fixed Point Theorems for ((mathfrak{F}); (phi)) - Contractive Mappings on C*-algebra Valued (mathfrak{B})-metric Spaces","authors":"K. Maheshwaran, R. J. Hussain, Nesrin Manav Tatar","doi":"10.9734/arjom/2023/v19i9713","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9713","url":null,"abstract":"This paper, we extends the new concept of common fixed point theorems in C*-algebra valued b-metric space (AV BMS) via ((mathfrak{F}); (phi)) - contractive mappings. Investigated are the common fixed points criteria for existence and uniqueness. Additionally, provide an illustrate an example.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116273860","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}
Pub Date : 2023-07-21DOI: 10.9734/arjom/2023/v19i9711
Dorathy O. Oramulu, Chinyere P. Igbokwe, I. C. Anabike, Harrison O. Etaga, Okechukwu J. Obulezi
In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.
{"title":"Simulation Study of the Bayesian and Non-Bayesian Estimation of a new Lifetime Distribution Parameters with Increasing Hazard Rate","authors":"Dorathy O. Oramulu, Chinyere P. Igbokwe, I. C. Anabike, Harrison O. Etaga, Okechukwu J. Obulezi","doi":"10.9734/arjom/2023/v19i9711","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9711","url":null,"abstract":"In this paper, a new distribution known as the Shifted Chris-Jerry (SHCJ) distribution is proposed. The proposition is motivated by the need to compare the efficiency of various classical estimation methods as well as the bayesian estimation using gamma prior at linear-exponential loss, squared error loss and generalized entropy loss functions. Some useful mathematical properties are derived. Single acceptance sampling plans (SASPs) are created for the distribution when the life test is truncated at a predetermined period. The median lifetime of the SHCJ distribution with pre-defined constants is taken as the truncation time. To guarantee that the specific life test is obtained at the defined risk to the user, the minimum sample size is required. For a particular consumer’s risk, the SHCJ distribution’s parameters, and the truncation time including numerical results are obtained. A simulation study is carried out for the bayesian and non-bayesian estimation of the parameters. Data on blood cancer patients is used to demonstrate the usefuleness of the proposed distribution.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114361298","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}
Pub Date : 2023-07-20DOI: 10.9734/arjom/2023/v19i9709
R. S. Das, Abhimanyu Kumar
In this article, we have combined two well known third order methods one is Chebyshev and another is Super- Halley to form an iterative method of third for solving polynomial equations with multiple polynomial zeros. This constructed method is basically the mean of the methods Chebyshev and Super-Halley, so we name the method as C-S Combined Mean Method. We have proposed some local convergence theorems of this C-S Combined Mean Method to establish the computation of a polynomial with known multiple zeros. For the establishment of this local convergence theorem, the key role is performed by a function(Real valued) termed as the function of initial conditions. Function of initial conditions I is a mapping from the set D into the set M , where D (subset of M ) is the domain of the C-S Combined mean iterative scheme. Here the initial conditions uses the information only at the initial point and are given in the form I(w0) which belongs to J , where J is an in interval on the positive real line which also contains 0 and w0 is the starting point. We have used the notion of gauge function which also plays very important role in establishing the convergence theorem. Here we have used two types of initial conditions over an arbitrary normed field and established local convergence theorems of the constructed C-S Combined mean method. The error estimations are also found in our convergence analysis. For simple zero, the method as well as the results hold good.
{"title":"Construction and Convergence of the C-S Combined Mean Method for Multiple Polynomial Zeros","authors":"R. S. Das, Abhimanyu Kumar","doi":"10.9734/arjom/2023/v19i9709","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9709","url":null,"abstract":"In this article, we have combined two well known third order methods one is Chebyshev and another is Super- Halley to form an iterative method of third for solving polynomial equations with multiple polynomial zeros. This constructed method is basically the mean of the methods Chebyshev and Super-Halley, so we name the method as C-S Combined Mean Method. We have proposed some local convergence theorems of this C-S Combined Mean Method to establish the computation of a polynomial with known multiple zeros. For the establishment of this local convergence theorem, the key role is performed by a function(Real valued) termed as the function of initial conditions. Function of initial conditions I is a mapping from the set D into the set M , where D (subset of M ) is the domain of the C-S Combined mean iterative scheme.\u0000Here the initial conditions uses the information only at the initial point and are given in the form I(w0) which belongs to J , where J is an in interval on the positive real line which also contains 0 and w0 is the starting point. We have used the notion of gauge function which also plays very important role in establishing the convergence theorem. Here we have used two types of initial conditions over an arbitrary normed field and established local convergence theorems of the constructed C-S Combined mean method. The error estimations are also found in our convergence analysis. For simple zero, the method as well as the results hold good.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127625725","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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