Vertex connectivity of the power graph of a finite cyclic group II

2018/10/25 by Sriparna Chattopadhyay, Kamal Lochan Patra, Chattopadhyay, Sriparna +3
Computer Science · Mathematics · #Interconnection Networks and Systems #Cooperative Communication and Network Coding #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1810.11316

Abstract

The power graph P(G) of a given finite group G is the simple undirected graph whose vertices are the elements of G, in which two distinct vertices are adjacent if and only if one of them can be obtained as an integral power of the other. The vertex connectivity κ(P(G)) of P(G) is the minimum number of vertices which need to be removed from G so that the induced subgraph of P(G) on the remaining vertices is disconnected or has only one vertex. For a positive integer n, let C_n be the cyclic group of order n. Suppose that the prime power decomposition of n is given by n =p₁^n₁p₂^n₂⋯ p_r^n_r, where r≥ 1, n₁,n₂,…, n_r are positive integers and p₁,p₂,…,p_r are prime numbers with p₁

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