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

1 Citation (Scopus)

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
Pages (from-to)	1210-1221
Number of pages	12
Journal	Indian Journal of Pure and Applied Mathematics
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s13226-023-00421-2
Publication status	Published - Dec 2024

Keywords

05C25
05C76
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

Cite this

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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.",

keywords = "05C25, 05C76, Automorphism, Co-normal product of graphs, Fixing set",

author = "\{ur Rehman\}, Shahid and Muhammad Imran and Imran Javaid",

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AU - ur Rehman, Shahid

AU - Imran, Muhammad

AU - Javaid, Imran

N1 - Publisher Copyright: © The Indian National Science Academy 2023.

PY - 2024/12

Y1 - 2024/12

N2 - 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.

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.

KW - 05C25

KW - 05C76

KW - Automorphism

KW - Co-normal product of graphs

KW - Fixing set

UR - https://www.scopus.com/pages/publications/85159359301

UR - https://www.scopus.com/pages/publications/85159359301#tab=citedBy

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DO - 10.1007/s13226-023-00421-2

M3 - Article

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JO - Indian Journal of Pure and Applied Mathematics

JF - Indian Journal of Pure and Applied Mathematics

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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