A graphs G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irred...

We formally introduce in this paper two parameters graph theory, namely, clique centrality and global centrality. Let G be a finite, simple undirected of order n. A is nonempty subset W \(\subseteq\) V (G) such that the subgraph \(\langle\)W\(\rangle\)G induced by complete. The maximum size any containing vertex u \(\in\) called G. Normalizing sum centralities all vertices will lead us to G, wh...

Iterated clique graphs arise when the clique operator is applied to a graph more than once. Determining whether a graph is a clique graph or an iterated clique graph is usually a difficult task. The fact that being a clique graph and being an iterated clique graph are not equivalent things has been proved recently. However, it is still unknown whether the classes of second iterated clique graph...

We consider a graph whose vertices are legally colored using k colors and ask if the contains -clique. As it turns out this very special type of -clique problem is in an intimate connection with constructing schedules. The practicality clique search based construction schedules checked by carrying numerical experiments.

A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of th...