Certain properties of the power graph associated with a finite group
TLDR
The power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other as mentioned in this paper.Abstract:
The power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other. The subgraph of is obtained by deleting the vertex 1 (the identity element of G). In this paper, we first investigate some properties of the power graph and its subgraph . We next provide necessary and sufficient conditions for a power graph to be a strongly regular graph, a bipartite graph or a planar graph. Finally, we obtain some infinite families of finite groups G for which the power graph contains some cut-edges.read more
Citations
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The structure and metric dimension of the power graph of a finite group
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On the chromatic number of the power graph of a finite group
Xuanlong Ma,Min Feng +1 more
TL;DR: In this paper, the chromatic number χ ( Γ G ) of a finite group G is investigated and a characterization of χ( ΓG ) is presented, and a conjecture in Mirzargar et al. is disproved.
References
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