Abstract The graph-parameters mainly studies vertex degree and distance between unordered vertices. There are many graph-parameters, this paper focuses on the Gutman index. For sake of discussion, puts forward concept “ contribution” based relationship index graph vertex-Gutman On basis, we discussed unicyclic with pendent edges in odd even parts, gave corresponding extremal graphs, which lays ...

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where are used to represent a group. One type graph representation group power graph. A G defined as whose vertex set all elements and two distinct vertices b adjacent if only or for positive integer . In addition mathematics, theory can be applied various fields science, one which chemistry, re...

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

Gutman proposed a new alternative interpretation of vertex-degree-based topological index, called Sombor index. It is defined via the term . In this paper, we determine explicit expressions index for line and total graphs several pericondensed benzenoid hydrocarbons.