Modified Detour Index of Hamiltonian Connected (Laceable) Graphs

Abstract

Objectives: To explore the bounds for the modified detour index of certain Hamiltonian connected and laceable graphs. Methods: The Wiener index , detour index and the modified detour index are used. Findings: Here we introduce the modified detour index and its least upper bounds for Hamiltonian connected and laceable graphs, by formulating the constraints. Novelty: Based on the modified detour index, the bounds for some special graphs such as: Hamiltonian connected graphs of two families of convex polytopes ( and ) and Hamiltonian laceable graphs of spider graph ( ) and image graph of prism graph ( ) are encountered here. Keywords: Hamiltonian graph, Hamiltonian connected, Hamiltonian laceable, Wiener index, detour index