On the order supergraph of the power graph of a finite group
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DOI: 10.1007/s11587-020-00520-w
Abstract: The power graph $${\mathcal {P}}_{G}$$ P G of a finite group G is the graph whose vertex set is G , two distinct vertices are adjacent if one is a power of the other. The… read more here.
Keywords: order supergraph; power; graph; finite group ... See more keywords
Characterizing finite nilpotent groups associated with a graph theoretic equality
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DOI: 10.1007/s11587-021-00655-4
Abstract: There are various graphs associated with groups which have been studied in the literature, e.g., Cayley graph, commuting graph, generating graph, prime graph. An interesting problem in this respect is to investigate the relation between… read more here.
Keywords: power graphs; group; power; graph ... See more keywords
Erratum: Vertex connectivity of the power graph of a finite cyclic group II
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DOI: 10.1142/s0219498820920012
Abstract: We retract [1, Lemma 3.4] as the statement is incorrect. In consequence, we correct the statements of Theorems 1.2 and 4.5 and their proofs. read more here.
Keywords: graph finite; erratum vertex; vertex connectivity; connectivity power ... See more keywords
On the minimum cut-sets of the power graph of a finite cyclic group
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DOI: 10.1142/s0219498824501767
Abstract: The power graph $\mathcal{P}(G)$ of a finite group $G$ is the simple graph with vertex set $G$, in which two distinct vertices are adjacent if one of them is a power of the other. For… read more here.
Keywords: group; cut sets; power graph; minimum cut ... See more keywords