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On some degree-and-distance-based graph invariants of trees

Author

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  • Gutman, Ivan
  • Furtula, Boris
  • Das, Kinkar Ch.

Abstract

Let G be a connected graph with vertex set V(G). For u, v ∈ V(G), d(v) and d(u, v) denote the degree of the vertex v and the distance between the vertices u and v. A much studied degree–and–distance–based graph invariant is the degree distance, defined as DD=∑{u,v}⊆V(G)[d(u)+d(v)]d(u,v). A related such invariant (usually called “Gutman index”) is ZZ=∑{u,v}⊆V(G)[d(u)·d(v)]d(u,v). If G is a tree, then both DD and ZZ are linearly related with the Wiener index W=∑{u,v}⊆V(G)d(u,v). We examine the difference DD−ZZ for trees and establish a number of regularities.

Suggested Citation

  • Gutman, Ivan & Furtula, Boris & Das, Kinkar Ch., 2016. "On some degree-and-distance-based graph invariants of trees," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 1-6.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:1-6
    DOI: 10.1016/j.amc.2016.04.040
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    Cited by:

    1. Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.

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