Gutman and Degree Monophonic Index of Graphs

Abstract

A graph with p points and q edges is denoted by G(p,q). An edge joining two non-adjacent points of a path P is called a chord of a path P. A path P is called monophonic if it is a chordless path. For any two points u and v in a connected graph G, the monophonic distance d (u,v) m from u to v is defined as the length of a longest u-v monophonic path in G. The Gutman monophonic index of a graph G is denoted by GutMP(G) and defined by GutMP(G) d(u)d(v)d (u,v) m and degree monophonic index of G is denoted by DMP(G) and defined by DMP(G) d(u) d(v)d (u,v)   m . The methodology executed in this research paper is to determine the monophonic distance matrix of graphs under consideration. The entries of monophonic distance matrix are calculated by counting the number of edges in the u-v monophonic path. In this paper for some standard graphs, GutMP(G) and DMP(G) are studied which can be applied to derive quantitative structure- property or structure- activity relationships (QSPR / QSAR).