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The contemporary literature cites Wiener index as a topological parameter associated with treelike molecular graphs derived from organic molecular structures. Given a graph G the corresponding Wiener index or total distance W(G) is defined as the sum of the graphic distances reckoned across all possible vertexpairs of G. Then W(G) of a graph G may be corelated to the physicochemical properties of an organic compound represented as G. This book explores some combinatorial and graph theoretic aspects of Wiener index of broad interest to practical Computer Scientists and Mathematicians. Such aspects are considered relevant to the process of drug synthesis and in the identification of lead drug candidates. It may be noted that the study of Wiener index and its variants are current areas of research from the standpoint of Mathematical Chemistry.
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