2019/09/25 by S. Morteza Mirafzal, Mirafzal, S. Morteza
Computer Science · Engineering · Mathematics · #05C25 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1909.11454
openalex publication_date 2019/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a graph with the vertex-set V and the edge-set E. Let N(v) denote the set of neighbors of the vertex v of G. The graph G is called irreducible whenever for every v,w ∈ V if v ≠ w, then N(v)≠ N(w). In this paper, we present a method for finding automorphism groups of connected bipartite irreducible graphs. Then, by our method, we determine automorphism groups of some classes of connected bipartite irreducible graphs, including a class of graphs which are derived from Grassmann graphs. Let a0 be a fixed positive integer. We show that if G is a connected non-bipartite irreducible graph such that c(v,w)=|N(v)∩ N(w)|=a0 when v,w are adjacent, whereas c(v,w) ≠ a0, when v,w are not adjacent, then G is a stable graph, that is, the automorphism group of the bipartite double cover of G is isomorphic with the group Aut(G) × ℤ2. Finally, we show that the Johnson graph J(n,k) is a stable graph.