Glasnik matematički, Vol. 47 No. 1, 2012.
Original scientific paper
https://doi.org/10.3336/gm.47.1.02
Relationship between edge Szeged and edge Wiener indices of graphs
Mohammad Javad Nadjafi-Arani
orcid.org/0000-0003-1754-6694
; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran
Hasan Khodashenas
; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran
Ali Reza Ashrafi
orcid.org/0000-0002-2858-0663
; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran
Abstract
Let G be a connected graph and ξ(G) = Sze(G) - We(G), where We(G) denotes the edge Wiener index and Sze(G) denotes the edge Szeged index of G. In an earlier paper, it is proved that if T is a tree then Sze(T) = We(T). In this paper, we continue our work to prove that for every connected graph G, Sze(G) ≥ We(G) with equality if and only if G is a tree. We also classify all graphs with ξ(G) ≤ 5. Finally, for each non-negative integer n ≠ 1 there exists a graph G such that ξ(G) = n.
Keywords
Edge Szeged index; edge Wiener index
Hrčak ID:
82568
URI
Publication date:
3.6.2012.
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