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

Author

Listed:
  • Shahid ur Rehman

    (Bahauddin Zakariya University)

  • Muhammad Imran

    (United Arab Emirates University)

  • Imran Javaid

    (Bahauddin Zakariya University)

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.

Suggested Citation

  • Shahid ur Rehman & Muhammad Imran & Imran Javaid, 2024. "On automorphisms and fixing number of co-normal product of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(4), pages 1210-1221, December.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:4:d:10.1007_s13226-023-00421-2
    DOI: 10.1007/s13226-023-00421-2
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    References listed on IDEAS

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    1. Dehmer, Matthias & Emmert-Streib, Frank & Mowshowitz, Abbe & Ilić, Aleksandar & Chen, Zengqiang & Yu, Guihai & Feng, Lihua & Ghorbani, Modjtaba & Varmuza, Kurt & Tao, Jin, 2020. "Relations and bounds for the zeros of graph polynomials using vertex orbits," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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