‎the second multiplicative zagreb coindex of a simple graph $g$ is‎ ‎defined as‎: ‎$${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$‎ ‎where $d_gleft(uright)$ denotes the degree of the vertex $u$ of‎ ‎$g$‎. ‎in this paper‎, ‎we compare $overline{{pi}}_2$-index with‎ ‎some well-known graph invariants such as the wiener index‎, ‎schultz‎ ‎index‎, ‎eccentric co...

let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

If G is a connected graph with vertex set V , then the eccentric connectivity index of G, ξ(G) is defined as ∑ deg(v).ec(v) where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The Wiener index W (G) = 1 2 [ ∑ d(u, v)], the hyper-Wiener index WW (G) = 1 2 [ ∑ d(u, v) + ∑ d(u, v)] and the reverseWiener index ∧(G) = n(n−1)D 2 −W (G), where d(u, v) is the distance of two vertice...

Let D be a digraph with vertex set V(D) .For vertex v V(D), the degree of v, denoted by d(v), is defined as the minimum value if its out-degree  and its in-degree . Now let D be a digraph with minimum degree  and edge-connectivity If  is real number, then the zeroth-order general Randic index is defined by   .  A digraph is maximally edge-connected if . In this paper we present sufficient condi...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.

The kth power of a graph G, denoted by Gk , is a graph with the same vertex set as G such that two vertices are adjacent in Gk if and only if their distance is at most k in G. The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. In this note, we give the bounds on the Wiener index of the graph Gk . The Nordhaus–Gaddum-t...

We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree. 2010 Mathematics Subject Classification : 05C90, 05C35.

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 reverse Wiener index of a connected graph G is defined as Λ(G) = 1 2 n(n− 1)d−W (G), where n is the number of vertices, d is the diameter, and W (G) is the Wiener index (the sum of distances between all unordered pairs of vertices) of G. We determine the n-vertex non-starlike trees with the first four largest reverse Wiener indices for n > 8, and the nvertex non-starlike non-caterpillar tre...