Geodesic
Generalized X-join of graphs and their automorphisms
Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article no. 06, 23 p.

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In this paper, we first introduce a new product of finite graphs as a generalization of the X-join of graphs.  We then give the necessary and sufficient conditions under which a graph has the  generalized X-join structure. As a main result, we compute the full automorphism groups of the family of graphs that have the generalized X-join structure.
DOI : 10.26493/1855-3974.2619.06c
Keywords: Automorphism, generalized wreath product, graph, lexicographic product, permutation group, X-join 
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Javad Bagherian; Hanieh Memarzadeh. Generalized X-join of graphs and their automorphisms. Ars Mathematica Contemporanea, Tome 24 (2024) no. 2, article  no. 06, 23 p. doi : 10.26493/1855-3974.2619.06c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2619.06c/

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