Certain properties of the power graph associated with a finite group

By A. Moghaddamfar, S. Rahbariyan, Wujie Shi. 2013

79 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0fca12df3ab748783c86813b4e44dcb823a0020c

Citations in the corpus

• A note on the power graph of a finite group (2016, unknown): “[15] considered the proper power graph P⋆(G).”