An Approach to Determination of Maximal Cliques in Undirected Graphs

Abstract

The article proposes the implicit exhaustive search procedure based on the triangle decomposition of graphs for determining the maximal clique in the arbitrary undirected graph G in polynomial time; it has allowed developing an exact algorithm for solving the problem with time complexity not exceeding ) ( 7 n O , where n is the number of vertices in the graph G.Index Terms-Мaximal independent set, click, vertex cover, decomposition of a graph into triangles 2 An Approach to Determination of Maximal Cliques in Undirected Graphs

Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry

“…We will also mention some modern works concerning aspects of neuro-nets with the use of the random graph models and biosimilar structures [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The latest technology and a conceptual approach to building neuron nets have resulted in network structures that capture the basic properties of cortical organization [11][12][13].…”

“…The study [22] proposes an implicit enumeration strategy for detecting the highest cluster in a random graph, relying on the triangular decomposition of topologies. The study [23] considers how graphs can be used to describe data.…”