Graph theory, a fundamental branch of mathematics, centers on the study of networks
composed of vertices (nodes) and edges, examining their paths, structures, and properties …

The Clay Mathematics Institute has selected seven Millennium Problems to motivate
research on important classic questions that have resisted solution over the years. Among …

The atom graph of a connected graph is a graph whose vertices are the atoms obtained by
clique minimal separator decomposition of this graph, and whose edges are the edges of all …

A biclique is a maximal set of vertices in a graph that induces a complete bipartite graph.
The biclique graph KB (G) of a graph G is the intersection graph of all bicliques in G. In this …

A\textit {biclique} is a maximal induced complete bipartite subgraph of $ G $. The\textit
{biclique graph} of a graph $ G $, denoted by $ KB (G) $, is the intersection graph of the …

We attach topological concepts to a simple graph by means of the simplicial complex of its
complete subgraphs. Using Forman's discrete Morse theory we show that the strong product …

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The edge-
biclique graph of G, KB e (G), is the edge-intersection graph of the bicliques of G. A graph G …

A biclique is a maximal induced complete bipartite subgraph. The biclique graph of a graph
H, denoted by KB (H), is the intersection graph of the family of all bicliques of H. In this work …

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The edge‐
biclique graph of G, KB e (G), is the edge‐intersection graph of the bicliques of G. A graph G …

The clique graph K (G) of a graph G is the intersection graph of all its (maximal) cliques. We
explore the effect of operations like edge contraction, edge removal and others on the …