Forbidden Subgraphs of co-prime Graphs of finite Groups

2023/01/25 by V V Swathi, V, Swathi, M S Sunitha +1
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2301.10422

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite group G the co-prime graph Γ(G) is defined as a graph with vertex set G in which two distinct vertices x and y are adjacent if and only if gcd(o(x),o(y))=1 where o(x) and o(y) denote the orders of the elements x and y respectively. In this paper we find properties of groups whose co-prime graphs forbid graphs such as C₄,K_1,3,P₄ and asteroidal triples.

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