A clique in an undirected graph G= (V, E) is a subset V ' ⊆ V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is NP-Complete. We have succeeded in developing a fast algorithm for maximum clique problem by employing the method of verification and elimination. For a graph o...

The spectral radius (or the signless Laplacian radius) of a general hypergraph is maximum modulus eigenvalues its adjacency Laplacian) tensor. In this paper, we firstly obtain lower bound hypergraphs in terms clique number. Moreover, present relation between homogeneous polynomial and number hypergraphs. As an application, finally upper

In this paper, we present a new fast architecture to compute the distance between cliques in different graphs. The distance obtained is used as a support function for graph labelling using probabflistic relaxation techniques. The architecture presented consists on a pipe-lined structure which computes the distance between an input clique and k reference cliques. The number of processing element...

Let G be a graph and KG be the set of all cliques of G, then the clique graph of G denoted by K(G) is the graph with vertex set KG and two elements Qi, Qj ∈ KG form an edge if and only if Qi ∩ Qj 6= ∅. Iterated clique graphs are defined by K0(G) = G, and K(G) = K(Kn−1(G)) for n > 0. In this paper we determine the number of cliques in K(G) when G = G1+G2, prove a necessary and sufficient conditi...

The congested clique is a synchronous, message-passing model of distributed computing in which each computational unit (node) in each round can send message of O(log n) bits to each other node of the network, where n is the number of nodes. This model has been considered under two extreme scanarios: unicast or broadcast. In the unicast model, a node can send (possibly) different message to each...

we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...