In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve problems existing in various disciplines physical sciences like computer sciences, physics, and chemistry. Topological indices (TIs) are one which frequently used identify different physicochemical structural properties molecular graphs. Wiener index is first distance-based TI that c...

‎the gutman index and degree distance of a connected graph $g$ are defined as‎ ‎begin{eqnarray*}‎ ‎textrm{gut}(g)=sum_{{u,v}subseteq v(g)}d(u)d(v)d_g(u,v)‎, ‎end{eqnarray*}‎ ‎and‎ ‎begin{eqnarray*}‎ ‎dd(g)=sum_{{u,v}subseteq v(g)}(d(u)+d(v))d_g(u,v)‎, ‎end{eqnarray*}‎ ‎respectively‎, ‎where‎ ‎$d(u)$ is the degree of vertex $u$ and $d_g(u,v)$ is the distance between vertices $u$ and $v$‎. ‎in th...

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 ...

In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.

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.