通过单边加法生成素数图:刻画一类图

IF 1 Q1 MATHEMATICS
Ayesha Alorini, Aymen Ben Amira, Mohammad Alzohairi, Moncef Bouaziz
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引用次数: 0

摘要

图G由顶点的有限集合V (G)和称为G的边缘集的不同顶点的无序对的集合E(G)组成,设G为图。一个顶点集合M是G的模,如果对于M中的顶点x和y以及M之外的每个顶点z, {z, x}∈E(G) < =⇒{z, y}∈E(G)。因此,G的一个模块是由M之外的顶点无法区分的顶点组成的集合M。空集、单集集和满集顶点表示平凡模块。如果一个图的所有模块都是平凡的,那么它是不可分解的,否则它是可分解的。至少有四个顶点的不可分解图是素图。对给定可分解图加一条边得到素数图的构造进行了介绍和研究,构成了本文的中心内容。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Prime Graph Generation through Single Edge Addition: Characterizing a Class of Graphs
A graph G consists of a finite set V (G) of vertices with a collection E(G) of unordered pairs of distinct vertices called edge set of G. Let G be a graph. A set M of vertices is a module of G if, for vertices x and y in M and each vertex z outside M, {z, x} ∈ E(G) ⇐⇒ {z, y} ∈ E(G). Thus, a module of G is a set M of vertices indistinguishable by the vertices outside M. The empty set, the singleton sets and the full set of vertices represent the trivial modules. A graph is indecomposable if all its modules are trivial, otherwise it is decomposable. Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decomposable graph by adding one edge constitue the central points of this paper.
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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