A greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empty. We have recently shown that any greedy clique decomposition of a graph of order n has at most-~ cliques. A greedy max-clique decomposition is a particular kind of greedy clique decomposition where maximum cliques are removed, instead of just maximal ones. In this pa...

A graph decomposition is a particular problem in the field of combinatorial designs (see Wallis [22] for more information on design theory). A graph decomposition of a graph H is a partition of the edge set of H . In this case, the graph H is called the host for the decomposition. Most graph decomposition problems are concerned with the case where every part of the partition is isomorphic to a ...

In this paper the performance of four well-known metaheuristics consisting of Artificial Bee Colony (ABC), Biogeographic Based Optimization (BBO), Harmony Search (HS) and Teaching Learning Based Optimization (TLBO) are investigated on optimal domain decomposition for parallel computing. A clique graph is used for transforming the connectivity of a finite element model (FEM) into that of the cor...

In this work, the solution of a boundary value problem is discussed via asemi analytical method. The purpose of the present paper is to inspect theapplication of the Adomian decomposition method for solving the Nagumo tele-graph equation. The numerical solution is obtained for some special cases sothat demonstrate the validity of method.

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

This article presents an unsupervised algorithm for word decomposition called UNGRADE (UNsupervised GRAph DEcomposition) to segment any word list of any language. UNGRADE assumes that each word follows the structure prefixes, a stem and suffixes without giving a limit on the number of prefixes and suffixes. The UNGRADE’s algorithm works in three steps and is language independent. Firstly, a pse...

A P -decomposition of a graph G is a set of pairwise edge-disjoint paths of G with edges that cover the edge set of G. Kotzig (1957) proved that a 3-regular graph admits a P3-decomposition if and only if it contains a perfect matching, and also asked what are the necessary and sufficient conditions for an -regular graph to admit a P -decomposition, for odd . Let g, and m be positive integers wi...