On π-Product Involution Graphs in Symmetric Groups

Peter Rowley; David Ward

doi:10.1007/s00373-015-1645-z

On π-Product Involution Graphs in Symmetric Groups

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose that G is a group, X a subset of G and π a set of natural numbers. The π-product graph Pπ(G,X) has X as its vertex set and distinct vertices are joined by an edge if the order of their product is in π. If X is a set of involutions, then Pπ(G,X) is called a π-product involution graph. In this paper we study the connectivity and diameters of Pπ(G,X) when G is a finite symmetric group and X is a G-conjugacy class of involutions.

Original language	English
Pages (from-to)	1545–1570
Journal	Graphs and Combinatorics
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s00373-015-1645-z
Publication status	Published - 2016

Keywords

Symmetric group
Product Graph
Diameter Connectedness

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AB - Suppose that G is a group, X a subset of G and π a set of natural numbers. The π-product graph Pπ(G,X) has X as its vertex set and distinct vertices are joined by an edge if the order of their product is in π. If X is a set of involutions, then Pπ(G,X) is called a π-product involution graph. In this paper we study the connectivity and diameters of Pπ(G,X) when G is a finite symmetric group and X is a G-conjugacy class of involutions.

KW - Symmetric group

KW - Product Graph

KW - Diameter Connectedness

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On π-Product Involution Graphs in Symmetric Groups

Abstract

Keywords

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