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Randić energy of specific graphs

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  • Alikhani, Saeid
  • Ghanbari, Nima

Abstract

Let G be a simple graph with vertex set V(G)={v1,v2,…,vn}. The Randić matrix of G, denoted by R(G), is defined as the n × n matrix whose (i, j)-entry is (didj)−12 if vi and vj are adjacent and 0 for another cases. Let the eigenvalues of the Randić matrix R(G) be ρ1 ≥ ρ2 ≥ ⋅⋅⋅ ≥ ρn which are the roots of the Randić characteristic polynomial ∏i=1n(ρ−ρi). The Randić energy RE of G is the sum of absolute values of the eigenvalues of R(G). In this paper, we compute the Randić characteristic polynomial and the Randić energy for specific graphs.

Suggested Citation

  • Alikhani, Saeid & Ghanbari, Nima, 2015. "Randić energy of specific graphs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 722-730.
  • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:722-730
    DOI: 10.1016/j.amc.2015.07.112
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    References listed on IDEAS

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    1. Dehmer, M. & Moosbrugger, M. & Shi, Y., 2015. "Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 164-168.
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    Cited by:

    1. Das, Kinkar Ch. & Mojallal, Seyed Ahmad, 2016. "Extremal Laplacian energy of threshold graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 267-280.

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