The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini an...

This paper proposes a new method, ConvGraph, to detect communities in highly cohesive and isolated weighted graphs, where the sum of weights is significantly higher inside than outside communities. The method starts by transforming original graph into line apply convolution, common technique computer vision field. Although this was originally conceived optimum edge images, it used here edges id...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted K2 (K2)bundles over a weighted graph F can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are F As an application, we compute the signature of a link whose corresponding weighted...

The purpose of the matching interdiction problem in a weighted graph is to find two vertices such that the weight of the maximum matching in the graph without these vertices is minimized. An approximate solution for this problem has been presented. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of...

An O(n log3 n) algorithm for the continuous p-center problem on a tree is presented. Following a sequence of previous algorithms, ours is the first one whose time bound in uniform in p and less than quadratic in n. We also present an O(n log2 n log log n) algorithm for a weighted discrete p-center problem. 1. Introduction. The p-center problems are defined on a weighted undirected graph G = (V,...

the purpose of the matching interdiction problem in a weighted graph is to findtwo vertices such that the weight of the maximum matching in the graph withoutthese vertices is minimized. an approximate solution for this problem has beenpresented. in this paper, we consider dendrimers as graphs such that the weightsof edges are the bond lengths. we obtain the maximum matching in some types ofdend...