We study eccentricity-based indices such as Zagreb eccentricity indices, general index and total index. present exact values of generalized networks related to binary $m$-ary trees, where $m \ge 2$.

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

In this paper, we prove the existence of fixed point for Chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this paper, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions a...

In 1982, Opsut showed that the competition number of a line graph is at most two and gave a necessary and sufficient condition for the competition number of a line graph being one. In this note, we generalize this result to the competition numbers of generalized line graphs, that is, we show that the competition number of a generalized line graph is at most two, and give necessary conditions an...

A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of bricks stems from the fact that they are building blocks of the matching decomposition procedure of Kotzig, and Lovász and Plummer. We prove that every brick except for the Petersen graph can be reduced to K4 or the prism by repeatedly applying a ce...

Structural approaches for pattern recognition frequently make use of graphs to represent objects. The concept of object similarity is of great importance in pattern recognition. The graph edit distance is often used to measure the similarity between two graphs. It basically consists in the amount of distortion needed to transform one graph into the other. The median graph of a set S of graphs i...

The generalized k-connectivity κk(G) of a graph G was introduced by Hager before 1985. As its a natural counterpart, we introduced the concept of generalized edge-connectivity λk(G), recently. In this paper we summarize the known results on the generalized connectivity and generalized edge-connectivity. After an introductory section, the paper is then divided into nine sections: the generalized...