On automorphisms and fixing number of co-normal product of graphs

Shahid ur Rehman (), Muhammad Imran () and Imran Javaid ()
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Shahid ur Rehman: Bahauddin Zakariya University
Muhammad Imran: United Arab Emirates University
Imran Javaid: Bahauddin Zakariya University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1210-1221

Abstract: Abstract An automorphism of a graph describes its structural symmetry and the concept of fixing number of a graph is used for breaking its symmetries (except the trivial one). In this paper, we evaluate automorphisms of the co-normal product graph $$G_1*G_2$$ G 1 ∗ G 2 of two simple graphs $$G_1$$ G 1 and $$G_2$$ G 2 and give sharp bounds on the order of its automorphism group. We study the fixing number of $$G_1*G_2$$ G 1 ∗ G 2 and prove sharp bounds on it. Moreover, we compute the fixing number of the co-normal product of some families of graphs.

Keywords: Fixing set; Automorphism; Co-normal product of graphs; 05C25; 05C76 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00421-2

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