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Please use this identifier to cite or link to this item: http://purl.org/purl/4220

Title: Equal opportunity networks, distance-balanced graphs, and Wiener game
Authors: Kannan, Balakrishnan
Aleksander, Vesel
Petra, Žigert Pleteršek
Manoj, Changat
Bostjan, Brešar
Sandi, Klavzar
Keywords: Wiener index
Equal opportunity network
Distance-balanced graph
Wiener game
Issue Date: 5-Feb-2014
Publisher: Elsevier
Abstract: Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.
Description: Discrete Optimization 12 (2014) 150–154
URI: http://dyuthi.cusat.ac.in/purl/4220
Appears in Collections:Dr. Kannan Balakrishnan

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