Construction of the enormous complete bipartite graphs and orthogonal double covers based on the Cartesian product

A. El-Mesady, T. Farahat, R. El-Shanawany
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Abstract

Let K be a graph with n vertices and G= { π(x) : x ∈v (K)} be a collection of isomorphic pages (called subgraphs) of K . Then G is an orthogonal double cover (ODC) of K by G iff (i) every edge of K is repeated exactly twice in G and (ii) π(a) and π(b) have one edge iff a and b are adjacent vertices in K . In this paper, we are interested in finding new symmetric starter vectors (SSV) based on Cartesian product methods, such as SSV of complete bipartite graphs with complete bipartite graphs, disjoint copies of paths with stars, stars with caterpillars, disjoint copies of stars with caterpillars, disjoint copies of cycles with caterpillars, disjoint copies of paths with caterpillars, and complete bipartite graphs with caterpillars. Then we use these symmetric starter vectors to get the enormous graphs and construct the ODCs.
基于笛卡尔积的巨大完全二部图和正交双盖的构造
设K是一个有n个顶点的图,G= {π(x): x∈v (K)}是K的同构页面(称为子图)的集合。那么G是K × G的正交双覆盖(ODC) (i) K的每条边在G和(ii)中重复两次π(a)和π(b)有一条边,如果a和b是K中的相邻顶点。本文研究了基于笛卡尔积方法的新的对称启动向量(SSV),如完全二部图与完全二部图的对称启动向量、带星路径的不相交复制、带毛虫的星路径的不相交复制、带毛虫的环的不相交复制、带毛虫的路径的不相交复制、带毛虫的完全二部图的对称启动向量。然后我们使用这些对称起始向量来得到巨大的图并构造odc。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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