منابع مشابه
On Harary Matrix, Harary Index and Harary Energy
Recently, a new molecular graph matrix, Harary matrix, was defined in honor of Professor Frank Harary, and new graph invariants (local and global) based on it were also defined and researched, Harary index is one of these invariants. The Harary matrix can be used to derive a variant of the Balaban index, Harary index was also successfully tested in several structure-property relationships, so i...
متن کاملCovering a graph with cuts of minimum total size
A cut in a graph G is the set of all edges between some set of vertices S and its complement S = V (G)− S. A cut-cover of G is a collection of cuts whose union is E(G) and the total size of a cut-cover is the sum of the number of edges of the cuts in the cover. The cut-cover size of a graph G, denoted by cs(G), is the minimum total size of a cut-cover of G. We give general bounds on cs(G), find...
متن کاملLaplacian Energy of a Fuzzy Graph
A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...
متن کاملLaplacian Sum-Eccentricity Energy of a Graph
We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...
متن کاملThe connectivity and the Harary index of a graph
The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paperweprovide anupper boundof theHarary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with themaximumHarary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In ad...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2014
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v90i3.10