general formulas are obtained for the vertex padmakar-ivan index (piv) of tetrathiafulvalene(ttf) dendrimer, whereby ttf units we are employed as branching centers. the piv index isa wiener-szeged-like index developed very recently. this topological index is defined as thesummation of all sums of nu(e) and nv(e), over all edges of connected graph g.

let $g$ be a connected graph with vertex set $v(g)$‎. ‎the‎ ‎degree resistance distance of $g$ is defined as $d_r(g) = sum_{{u‎,‎v} subseteq v(g)} [d(u)+d(v)] r(u,v)$‎, ‎where $d(u)$ is the degree‎ ‎of vertex $u$‎, ‎and $r(u,v)$ denotes the resistance distance between‎ ‎$u$ and $v$‎. ‎in this paper‎, ‎we characterize $n$-vertex unicyclic‎ ‎graphs having minimum and second minimum degree resista...

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.

Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.

A hypergraph is said to be oriented if each edge-vertex incidence has a label of +1 or −1. An called balanced there exists bipartition the vertex set such that every edge intersects one part in positively incident vertices with and other negatively edge. In this paper, we investigate balance hypergraphs induced signed by means eigenvalues associated matrices tensors provide spectral method char...

Let [Formula: see text] be a graph. A set [Formula: see text] is a distance k-dominating set of G if for every vertex [Formula: see text], [Formula: see text] for some vertex [Formula: see text], where k is a positive integer. The distance k-domination number [Formula: see text] of G is the minimum cardinality among all distance k-dominating sets of G. The first Zagreb index of G is defined as ...

Let G and H be connected graphs. The tensor product G + H is a graph with vertex set V(G+H) = V (G) X V(H) and edge set E(G + H) ={(a , b)(x , y)| ax ∈ E(G) & by ∈ E(H)}. The graph H is called the strongly triangular if for every vertex u and v there exists a vertex w adjacent to both of them. In this article the tensor product of G + H under some distancebased topological indices are investiga...

A graph G is vertex pancyclic if for each vertex v ∈ V (G), and for each integer k with 3 ≤ k ≤ |V (G)|, G has a k-cycle Ck such that v ∈ V (Ck). Let s ≥ 0 be an integer. If the removal of at most s vertices in G results in a vertex pancyclic graph, we say G is an s-vertex pancyclic graph. Let G be a simple connected graph that is not a path, cycle or K1,3. Let l(G) = max{m : G has a divalent p...