ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 24 (2024) #P2.06
https://doi.org/10.26493/1855-3974.2619.06c
(Also available at http://amc-journal.eu)
Generalized X-join of graphs and their
automorphisms*
Javad Bagherian †, Hanieh Memarzadeh
Department of Pure Mathematics, Faculty of Mathematics and Statistics,
University of Isfahan, P.O. Box: 81746-73441, Isfahan, Iran
Received 4 May 2021, accepted 6 April 2023, published online 27 September 2023
Abstract
In this paper, we first introduce a new product of finite graphs as a generalization of
the X-join of graphs. We then give necessary and sufficient conditions for a graph to be
isomorphic to a generalized X-join. As a main result, we give necessary and sufficient
conditions under which the full automorphism group of a generalized X-join is equal to the
generalized wreath product of the automorphism groups of its factors.
Keywords: Automorphism, generalized wreath product, graph, lexicographic product, permutation
group, X-join.
Math. Subj. Class. (2020): 05C25, 20B25, 20E22
*The authors are grateful to the anonymous referees, whose comprehensive reports helped to improve the
quality of this paper.
†Corresponding author.
E-mail addresses: bagherian@sci.ui.ac.ir (Javad Bagherian), h.memarzadeh.762@sci.ui.ac.ir (Hanieh
Memarzadeh)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 1855-3966 (tiskana izd.), ISSN 1855-3974 (elektronska izd.)
ARS MATHEMATICA CONTEMPORANEA 24 (2024) #P2.06
https://doi.org/10.26493/1855-3974.2619.06c
(Dostopno tudi na http://amc-journal.eu)
Posplošeni X-spoji grafov in njihovi
avtomorfizmi*
Javad Bagherian †, Hanieh Memarzadeh
Department of Pure Mathematics, Faculty of Mathematics and Statistics,
University of Isfahan, P.O. Box: 81746-73441, Isfahan, Iran
Prejeto 4. maja 2021, sprejeto 6. aprila 2023, objavljeno na spletu 27. septembra 2023
Povzetek
V tem članku najprej vpeljemo nov produkt končnih grafov kot posplošitev X-spoja
grafov. Potem podamo potrebne in zadostne pogoje za to, da je graf izomorfen posplošen-
emu X-spoju. Kot glavni rezultat, podamo potrebne in zadostne pogoje za to, da je polna
grupa avtomorfizmov posplošenega X-spoja enaka posplošenemu venčnemu produktu grup
avtomorfizmov njegovih faktorjev.
Ključne besede: Avtomorfizem, posplošeni venčni produkt, graf, leksikografski produkt, permutaci-
jska grupa, X-spoj.
Math. Subj. Class. (2020): 05C25, 20B25, 20E22
*Avtorji so hvaležni anonimnim recenzentom, katerih izčrpna poročila so pomagala izboljšati kakovost tega
članka.
†Kontaktni avtor.
E-poštna naslova: bagherian@sci.ui.ac.ir (Javad Bagherian), h.memarzadeh.762@sci.ui.ac.ir (Hanieh
Memarzadeh)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/