Automorphisms of linear functional graphs over vector spaces

2020/06/15 by Majidinya, Ali · 1 citation
#05C25 #05C50 #Combinatorics (math.CO) #F.2.1 #F.2.2 #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.08201

Abstract

Let \mathbbF_q be a finite field with q elements, n≥2 a positive integer, \mathbbV₀ a n-dimensional vector space over \mathbbF_q and \mathbbT₀ the set of all linear functionals from \mathbbV₀ to \mathbbF_q. Let \mathbbV=\mathbbV₀∖\0\ and \mathbbT=\mathbbT₀∖\0\. The linear functional graph of \mathbbV₀ dented by \digamma(\mathbbV), is an undirected bipartite graph, whose vertex set V is partitioned into two sets as V=\mathbbV∪ \mathbbT and two vertices v∈ \mathbbV and f∈ \mathbbT are adjacent if and only if f sends v to the zero element of \mathbbF_q (i.e. f(v)=0). In this paper, the structure of all automorphisms of this graph is characterized and formolized. Also the cardinal number of automorphisms group for this graph is determined.

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