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- W3088032306 abstract "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 $$v,w in V$$ if $$v ne w$$ , then $$N(v)ne N(w).$$ 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 $$a_0$$ be a fixed positive integer. We show that if G is a connected non-bipartite irreducible graph such that $$c(v,w)=|N(v)cap N(w)|=a_0$$ when v, w are adjacent, whereas $$c(v,w) ne a_0$$ , 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 $${mathrm{Aut}}(G) times {mathbb {Z}}_2$$ . Finally, we show that the Johnson graph J(n, k) is a stable graph." @default.
- W3088032306 created "2020-10-01" @default.
- W3088032306 creator A5030253418 @default.
- W3088032306 date "2020-09-19" @default.
- W3088032306 modified "2023-10-03" @default.
- W3088032306 title "On the automorphism groups of connected bipartite irreducible graphs" @default.
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- W3088032306 doi "https://doi.org/10.1007/s12044-020-00589-1" @default.
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