Sparse matrix-matrix products appear in multigrid solvers and computational methods for graph theory. Some formulations of these products require the inner product of two sparse vectors, which have inefficient use of cache memory. In this paper, we propose a new algorithm for computing sparse matrix-matrix products by exploiting matrix nonzero structure through the process of graph coloring. We...

Szemerédi’s regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and Rödl proved an analogue of Szemerédi’s regularity lemma for sparse graphs as part of a general program toward extending extremal results to sparse graphs. Many of the key applications of Szemerédi’s regularity lemma us...

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 ...

in this article, the results of special effects of privatization of iranian gas refining industry with delphi-dematel integrative approach are presented. according to the results of this research in delphi technique base, all together, experts recognize 39 pivotal factors in privatization of the gas refining companies. then by the aids of dematel technique, in previous step, according to expert...

We investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ $L(F)$ of graphs $E$ $F$ over a commutative ground ring $\ell$. approach this by studying structure such under bivariant algebraic $K$-theory $kk$, which is universal theory with properties above. show that very mild assumptions on $\ell$, ...

the first geometric-arithmetic index was introduced in the chemical theory as the summationof 2 du dv /(du  dv ) overall edges of the graph, where du stand for the degree of the vertexu. in this paper we give the expressions for computing the first geometric-arithmetic index ofhexagonal systems and phenylenes and present new method for describing hexagonal systemby corresponding a simple graph...