Abstract
Let G be a connected n-vertex graph with the vertex set V(G) = {v 1, v 2, โฆ, v n } and let P = (p 1, p 2, โฆ, p n ) be an n-tuple of nonnegative integers. The thorn graph G P is the graph obtained by attaching p i new vertices of degree one to the vertex v i of G, for i = 1, 2, โฆ, n. In this paper, relations between the edge-Wiener indices of G and G P have been established and several special cases of these results have been examined. Results are applied to obtain closed formulas for the terminal Wiener index, the first and the second edge-Wiener indices of an infinite family of dendrimers by considering them as thorn graphs of simpler dendrimers.
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