The eccentric sequence of a connected graph \(G\) is the nondecreasing eccentricities its vertices. Wiener index sum distances between all unordered pairs vertices \(G\). unique trees that minimise among with given were recently determined by present authors. In this paper we show these results hold not only for index, but large class distance-based topological indices which term Wiener-type in...

Topological indices are numbers that applied to a graph and can be used describe specific properties through algebraic structures. Algebraic theory is helpful tool in range of chemistry domains. Because it helps explain how the different symmetries molecules crystals affect their structure dynamics, powerful theoretical approach for forecasting both common uncommon characteristics molecules. A ...

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)...

A novel unsymmetric square matrix, WPU , is proposed for calculating both Wiener, W , and hyper-Wiener, WW, numbers. This matrix is constructed by using single endpoint characterization of paths. Its relations with Wiener-type numbers are discussed.

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

Let G be a simple connected molecular graph with vertex set V(G) and edge set E(G). One important modification of classical Zagreb index, called hyper Zagreb index HM(G) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms 2 [ ( ) ( )] G G d u d v  over all the edges of G, where ( ) G d u denote the degree of the vetex u of G. In this paper, th...

For a (molecular) graph, the hyper Zagreb index is defined as HM(G) = ∑ uv∈E(G) (dG(u) + dG(v)) 2 and the hyper Zagreb coindex is defined asHM(G) = ∑ uv/ ∈E(G) (dG(u)+dG(v)) 2. In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.