let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur'{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graph...

Let be any connected graph with vertices set and edges . For two distinct , the detour distance between which is denoted by a longest path in The polynomial of ; defined In this paper, theta uniform will computed.

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.

The k-th semi total point graph of a graph G, , ‎is a graph‎ obtained from G by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎In this paper‎, a formula for Laplacian polynomial of in terms of‎ characteristic and Laplacian polynomials of G is computed‎, ‎where is a connected regular graph‎.The Kirchhoff index of is also computed‎.

the harmonic index h(g) , of a graph g is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in e(g), where deg (u) denotes the degree of a vertex u in v(g). in this paper we define the harmonic polynomial of g. we present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in caterpill...

let $g$ be a simple graph of order $n$. the domination polynomial of $g$ is the polynomial $d(g, x)=sum_{i=gamma(g)}^{n} d(g,i) x^{i}$, where $d(g,i)$ is the number of dominating sets of $g$ of size $i$ and $gamma(g)$ is the domination number of $g$. in this paper we present some families of graphs whose domination polynomials are unimodal.