A study on detour concepts in graphs and their applications

Abstract

iiii newlineABSTRACT newlineDistance is a concept that runs through all of graph theory, and it s newlineemployed in isomorphism tests, graph operations, hamiltonicity difficulties, newlineextremal connectivity problems, diameter, and convexity in graphs. The length newlineof the longest u v path in G is the detour distance l(u,v) between two vertices newlineu and v in a connected graph G. A molecular graph, a labelled graph whose newlinevertex and edge labels describe the atom and bond types, can be used to newlinerepresent the structure of a chemical compound. Topological indices are graph newlineinvariants defined to analyze the drug molecular structures and pharmacy newlinecharacteristics, such as melting point, boiling point, and other biochemical newlineactivities. Computational chemistry is a discipline of chemistry that deals with newlineutilizing mathematical methods to compute and model molecular behaviour and newlineproperties. The detour index is one of the topological index in the collection of newlinecomputational chemistry works. newlineIn this thesis we contribute to the literature of computational newlinechemistry by providing exact expressions for the detour index of joins of newlineHamilton-Connected (HC) graphs. This improves on previous results by newlinerequiring only particular subgraphs of a molecular network to be Hamilton- newlineconnected, rather than the entire molecular graph. We have also calculated the newline