Implementing graph algorithms efficiently in a rule-based language is challenging because pattern matching expensive. In this paper, we present number of linear-time implementations GP 2, an experimental programming based on transformation rules which aims to facilitate program analysis and verification. We focus two classes programs: reduction programs check some property, using depth-first se...

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

university course timetabling is a complex optimizationproblem. there are many components like departments, faculties, rooms,and students making the problem huge and difficult to solve. eachcomponent enforces a set of normally conflicting constraints on thesolution space. the problem will be solved if courses are scheduled indifferent rooms and within some specific time slots such that a set of...

we present a matching and lp based heuristic algorithm that decides graph non-hamiltonicity. each of the n! hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices p, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. a graph instance (g) is initially coded as exclusion set ...

In mathematical chemistry, a particular attention is given to degree-based graph invariant. The Zagrebpolynomial is one of the degree based polynomials considered in chemical graph theory. A dendrimer isan artificially manufactured or synthesized molecule built up from branched units called monomers. Inthis note, the first, second and third Zagreb poly...