Let G and H be two graphs. The corona product G o H is obtained by taking one copy of G and |V(G)| copies of H; and by joining each vertex of the i-th copy of H to the i-th vertex of G, i = 1, 2, …, |V(G)|. In this paper, we compute PI and hyper–Wiener indices of the corona product of graphs.

The edge-Wiener index of a connected graph is the sum of the distances between all pairs of edges of the graph. In this paper, we determine the polyphenyl chains with minimum and maximum edge-Wiener indices among all the polyphenyl chains with h hexagons. Moreover, explicit formulas for the edge-Wiener indices of extremal polyphenyl chains are obtained.

Let $G$ be a molecular graph with vertex set $V(G)$, $d_G(u, v)$ the topological distance between vertices $u$ and $v$ in $G$. The Hosoya polynomial $H(G, x)$ of $G$ is a polynomial $sumlimits_{{u, v}subseteq V(G)}x^{d_G(u, v)}$ in variable $x$. In this paper, we obtain an explicit analytical expression for the expected value of the Hosoya polynomial of a random benzenoid chain with $n$ hexagon...

The Hosoya polynomial of a graph, H(G, z), has the property that its first derivative, evaluated at z = 1, equals the Wiener index, i.e., W(G) = H’(G, 1). In this paper, an equation is presented that gives the hyper-Wiener index, WW(G), in terms of the first and second derivatives of H(G,z). Also defined here is a hyper-Hosoya polynomial, HH(G,r), which has the property WW(G) = HH’(G, l), analo...

This paper deals with the study of the Malliavin calculus of Euclidean motions on Wiener space, (i.e. transformations induced by general measure preserving transformations, called 'rotations', and H-valued shifts) and the associated flows on abstract Wiener spaces.

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

The diffraction by impenetrable wedges having arbitrary aperture angle is studied by means of the Wiener-Hopf (W-H) technique. A system of functional equations called generalized Wiener-Hopf equations (GWHE) is obtained. Only for certain values of the aperture angle these equations are recognizable as standard or classical Wiener-Hopf equations (CWHE). However, in all cases, a mapping to a suit...

Let G and H be graphs. The strong product G⊠H of graphs G and H is the graph with vertex set V (G) × V (H) and u = (u1, v1) is adjacent with v = (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we study some properties of this operation. Also, we obtain lower and upper bounds for...

Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...