the wiener index w(g) of a connected graph g is defined as the sum of the distances betweenall unordered pairs of vertices of g. the eccentricity of a vertex v in g is the distance to avertex farthest from v. in this paper we obtain the wiener index of a graph in terms ofeccentricities. further we extend these results to the self-centered graphs.

The distance $d(u,v)$ between two vertices $u$ and $v$ of a graph $G$ is equal to the length of a shortest path that connects $u$ and $v$. Define $WW(G,x) = 1/2sum_{{ a,b } subseteq V(G)}x^{d(a,b) + d^2(a,b)}$, where $d(G)$ is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are compu...

In this paper, we give a survey of methods used to calculate values resistance distance (also known as effective resistance) in graphs. Resistance has played prominent role not only circuit theory and chemistry, but also combinatorial matrix spectral graph theory. Moreover applications ranging from quantifying biological structures, distributed control systems, network analysis, power grid syst...

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...