The concept of the Gutman index, denoted Gut(G) was introduced for a connected undirected graph G. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (directed graphs by definition), and decribe a recursive formula for the Gutman index Gut(J∗ n+1(1)) in terms of the Gutman index of the underlying Jaco graph, J ∗ n (1), n ∈ N with prime Jaconian vertex vi. W...

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric−arithmetic index of graphs, Iran. J. Math Chem., 1 (2010) 17−27, in this paper we present lower and upper bounds on the third geometric−arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus−Gaddum−type result for GA3.

Recently, it was conjectured by Gutman and Ashrafi that the complete graph Kn has the greatest edge-Szeged index among simple graphs with n vertices. This conjecture turned out to be false, but led Vukičević to conjecture the coefficient 1/15552 of n6 for the approximate value of the greatest edge-Szeged index. We provide counterexamples to this conjecture.

 The work is supported by Training and plan projects of college students' innovation and pioneering in Guangdong Province(No.1056412059). Abstract Wiener index proposed by Harold Wiener in 1947 is a very important topological index which is widely applied in chemical research. Gutman et al. extended the Wiener index to variable Wiener index. M. H. Liu et al. obtained the maximum variable Wiene...

Sombor index of a graph is novel invariant which was introduced by Gutman and stated as SO (G)=Σuv∈E(du2+dv2) where du dV are the degree vertices u v respectively. In this article, we have computed index, Reduced Banhatti sombor Graphene.

Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative St...

The Wiener indexW (G) of a connected graphG is defined to be the sum ∑ u,v d(u, v) of the distances between the pairs of vertices in G. Similarly, the edge-Wiener index We(G) of G is defined to be the sum ∑ e,f d(e, f) of the distances between the pairs of edges in G, or equivalently, the Wiener index of the line graph L(G). Finally, the Gutman index Gut(G) is defined to be the sum ∑ u,v deg(u)...