A vertex labeling (xi) of a graph (chi) is referred to as a 'vertex equitable labeling (VEq.)' if the induced edge weights, obtained by summing the labels of the end vertices, satisfy the following condition: the absolute difference in the number of vertices (v) and (u) with labels (xi(v)= a) and (xi(u)= b) (where (a, bin Z)) is approximately (1), considering a given set (A) that consists of the first (lceil frac{q}{2} rceil) non-negative integers. A graph $chi$ that admits a vertex equitable labeling (VEq.) is termed a 'vertex equitable' graph. In this manuscript, we have demonstrated that graphs related to cycles and paths are examples of vertex-equitable graphs.
图（chi）的顶点标记（neneneba xi ）被称为“顶点公平标记（VEq.）”，如果通过对末端顶点的标签求和而获得的诱导边权重满足以下条件：具有标签（nenenebb xi（v）=A）和（nenenebc xi（u）=b）（其中在Z中（A，b））的顶点数量的绝对差约为（1），考虑由第一个非负整数组成的给定集合（a）。允许顶点公平标记（VEq.）的图$chi$被称为“顶点公平”图。在这篇手稿中，我们已经证明了与循环和路径相关的图是顶点公平图的例子。
{"title":"Cycles and Paths Related Vertex-Equitable Graphs","authors":"S. Nazeer, Najma Sultana, E. Bonyah","doi":"10.61091/jcmcc117-02","DOIUrl":"https://doi.org/10.61091/jcmcc117-02","url":null,"abstract":"A vertex labeling (xi) of a graph (chi) is referred to as a 'vertex equitable labeling (VEq.)' if the induced edge weights, obtained by summing the labels of the end vertices, satisfy the following condition: the absolute difference in the number of vertices (v) and (u) with labels (xi(v)= a) and (xi(u)= b) (where (a, bin Z)) is approximately (1), considering a given set (A) that consists of the first (lceil frac{q}{2} rceil) non-negative integers. A graph $chi$ that admits a vertex equitable labeling (VEq.) is termed a 'vertex equitable' graph. In this manuscript, we have demonstrated that graphs related to cycles and paths are examples of vertex-equitable graphs.","PeriodicalId":39040,"journal":{"name":"Journal of Combinatorial Mathematics and Combinatorial Computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44295034","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}
Network theory is the study of graphs such as representing equilibrium relationships or unequal relationships between different objects. A network can be defined as a graph where nodes and / or margins have attributes (e.g. words). Topological index of a graph is a number that helps to understand its topology and a topological index is known as irregularity index if it is greater than zero and topological index of graph is equal to zero if and only if graph is regular. The irregularity indices are used for computational analysis of nonregular graph topological composition. In this paper, we aim to compute topological invariants of some computer related graph networks. We computed various irregularities indices for the graphs of OTIS swapped network (OP_a) and Biswapped Networks (Bsw(Pa).)
{"title":"Study of Topological Behavior of Some Computer Related Graphs","authors":"Xiaohui Ren, I. Ahmed, Rui Liu","doi":"10.61091/jcmcc117-01","DOIUrl":"https://doi.org/10.61091/jcmcc117-01","url":null,"abstract":"Network theory is the study of graphs such as representing equilibrium relationships or unequal relationships between different objects. A network can be defined as a graph where nodes and / or margins have attributes (e.g. words). Topological index of a graph is a number that helps to understand its topology and a topological index is known as irregularity index if it is greater than zero and topological index of graph is equal to zero if and only if graph is regular. The irregularity indices are used for computational analysis of nonregular graph topological composition. In this paper, we aim to compute topological invariants of some computer related graph networks. We computed various irregularities indices for the graphs of OTIS swapped network (OP_a) and Biswapped Networks (Bsw(Pa).)","PeriodicalId":39040,"journal":{"name":"Journal of Combinatorial Mathematics and Combinatorial Computing","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44445007","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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