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Distance powers of unitary Cayley graphs

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  • Liu, Xiaogang
  • Li, Binlong

Abstract

Let G be a graph and let diam(G) denote the diameter of G. The distance power GN of G is the undirected graph with vertex set V(G), in which x and y are adjacent if their distance d(x, y) in G belongs to N, where N is a non-empty subset of {1,2,…,diam(G)}. The unitary Cayley graph is the graph having the vertex set Zn and the edge set {(a,b):a,b∈Zn,gcd(a−b,n)=1}. In this paper, we determine the energies of distance powers of unitary Cayley graphs, and classify all Ramanujan distance powers of unitary Cayley graphs. By the energies of distance powers of unitary Cayley graphs, we construct infinitely many pairs of non-cospectral equienergetic graphs. Moreover, we characterize all hyperenergetic distance powers of unitary Cayley graphs.

Suggested Citation

  • Liu, Xiaogang & Li, Binlong, 2016. "Distance powers of unitary Cayley graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 272-280.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:272-280
    DOI: 10.1016/j.amc.2016.05.023
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    Cited by:

    1. Yipeng Li & Jing Zhang & Meili Wang, 2023. "The Square of Some Generalized Hamming Graphs," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    2. T. Tamizh Chelvam & S. Anukumar Kathirvel & M. Balamurugan, 2020. "Domination in generalized unit and unitary Cayley graphs of finite rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 533-556, June.
    3. S. Madhumitha & Sudev Naduvath, 2023. "Graphs Defined on Rings: A Review," Mathematics, MDPI, vol. 11(17), pages 1-80, August.

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