A topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. A new counting polynomial, called the "Omega" W(G, x) polynomial, was recently proposed by Diudea on the ground of quasi-orthogonal cut "qoc" edge strips in a polycyclic graph. In this paper, the vertex PI, Szeged and omega polynomials of carbon nanocones CNC4[n] are computed.

the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...

In chemical graph theory, many graph parameters, or topological indices, were proposed as estimators of molecular structural properties. Often several variants of an index are considered. The aim is to extend the original concept to larger families of graphs than initially considered, or to make it more precise and discriminant, or yet to make its range of values similar to that of another inde...

We show that on cactus graphs the Szeged index is bounded above by twice Wiener index. For revised situation reversed if graph class further restricted. Namely, all blocks of a are cycles, then its below Additionally, we these bounds sharp and examine cases equality. Along way, provide formulation as sum over vertices, which proves very helpful, may be interesting in other contexts.

Let G be a graph with vertex and edge sets V(G) and E(G), respectively. As usual, the distance between the vertices u and v of a connected graph G is denoted by d(u,v) and it is defined as the number of edges in a minimal path connecting the vertices u and v. Throughout the paper, a graph means undirected connected graph without loops and multiple edges. In chemical graph theory, a molecular gr...

hansen et‎. ‎al.‎, ‎using the autographix software ‎package‎, ‎conjectured that the szeged index $sz(g)$ and the‎ ‎wiener index $w(g)$ of a connected bipartite graph $g$ with $n geq ‎4$ vertices and $m geq n$ edges‎, ‎obeys the relation‎ ‎$sz(g)-w(g) geq 4n-8$‎. ‎moreover‎, ‎this bound would be the best possible‎. ‎this paper offers a proof to this conjecture‎.

topological indices are numerical parameters of a graph which characterize its topology. inthis paper the pi, szeged and zagreb group indices of the tetrameric 1,3–adamantane arecomputed.