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

Shahid ur Rehman; Muhammad Imran; Imran Javaid

doi:10.1007/s13226-023-00421-2

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

Shahid ur Rehman, Muhammad Imran, Imran Javaid

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 G₁∗ G₂ of two simple graphs G₁ and G₂ and give sharp bounds on the order of its automorphism group. We study the fixing number of G₁∗ G₂ and prove sharp bounds on it. Moreover, we compute the fixing number of the co-normal product of some families of graphs.

Original language	English
Journal	Indian Journal of Pure and Applied Mathematics
DOIs	https://doi.org/10.1007/s13226-023-00421-2
Publication status	Accepted/In press - 2023

Keywords

Automorphism
Co-normal product of graphs
Fixing set

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s13226-023-00421-2

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AB - 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 G1∗ G2 of two simple graphs G1 and G2 and give sharp bounds on the order of its automorphism group. We study the fixing number of G1∗ G2 and prove sharp bounds on it. Moreover, we compute the fixing number of the co-normal product of some families of graphs.

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KW - Co-normal product of graphs

KW - Fixing set

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JF - Indian Journal of Pure and Applied Mathematics

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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