Given a connected graph Δ, a group G can be constructed in such a way that Δ is often isomorphic to a subgraph of the commuting graph KG(G) of G. We show that, with one exception, KG(G) is connected, and in this latter case its diameter is at most that of Δ. If Δ is a path of length n>2 then diam(KG(G))=n.
On a construction by Giudici and Parker on commuting graphs of groups / Cutolo, Giovanni. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - 192:(2022), p. 105666. [10.1016/j.jcta.2022.105666]
On a construction by Giudici and Parker on commuting graphs of groups
Giovanni Cutolo
Primo
2022
Abstract
Given a connected graph Δ, a group G can be constructed in such a way that Δ is often isomorphic to a subgraph of the commuting graph KG(G) of G. We show that, with one exception, KG(G) is connected, and in this latter case its diameter is at most that of Δ. If Δ is a path of length n>2 then diam(KG(G))=n.File in questo prodotto:
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