THE REVISED EDGE SZEGED INDEX OF BRIDGE GRAPHS

Authors : Hui DONG ,  bo ZHOU

Pages : 559-566

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Publication Date : 2012-04-01

Article Type : Research Paper

Abstract :The revised edge Szeged index of a connected graph G is defined as Sz∗ e insert ignore into journalissuearticles values(G); = X e=uv∈Einsert ignore into journalissuearticles values(G); muinsert ignore into journalissuearticles values(e|G); + m0insert ignore into journalissuearticles values(e|G); 2 mvinsert ignore into journalissuearticles values(e|G); + m0insert ignore into journalissuearticles values(e|G); 2 , where Einsert ignore into journalissuearticles values(G); is the edge set of G, muinsert ignore into journalissuearticles values(e|G); is the number of edges closer to vertex u than to vertex v in G, mvinsert ignore into journalissuearticles values(e|G); is the number of edges closer to vertex v than to vertex u in G, and m0insert ignore into journalissuearticles values(e|G); is the number of edges equidistant from both ends of e. We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.
Keywords : Szeged index, Revised edge Szeged index, Revised Szeged index, Bridge graphs, Distance, 2000 AMS Classification 05 C 12