Automorphisms of linear functional graphs over vector spaces

Abstract

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