Let graph energy is a graph--spectrum--based quantity‎, ‎introduced in the 1970s‎. ‎After a latent period of 20--30 years‎, ‎it became a popular topic of research both‎ ‎in mathematical chemistry and in ``pure'' spectral graph theory‎, ‎resulting in‎ ‎over 600 published papers‎. ‎Eventually‎, ‎scores of different graph energies have‎ ‎been conceived‎. ‎In this article we...

the chromatic number of a graph g, denoted by χ(g), is the minimum number of colors such that g can be colored with these colors in such a way that no two adjacent vertices have the same color. a clique in a graph is a set of mutually adjacent vertices. the maximum size of a clique in a graph g is called the clique number of g. the turán graph tn(k) is a complete k-partite graph whose partition...

Web services as independent software components are published on the Internet by service providers and services are then called by users’ request. However, in many cases, no service alone can be found in the service repository that could satisfy the applicant satisfaction. Service composition provides new components by using an interactive model to accelerate the programs. Prior to service comp...

A novel method for comparing non-aligned graphs of various sizes is proposed, based on the Wasserstein distance between graph signal distributions induced by respective Laplacian matrices. Specifically, a new formulation one-to-many alignment problem casted, which aims at matching node in smaller with one or more nodes larger graph. By incorporating optimal transport into our comparison framewo...

Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$,  if no two vertices of $S$ are adjacent.The  independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.