Sphere of influence graphs: Edge density and clique size

Clique Graphs and Edge-clique graphs

Not every edge-clique graph is a clique graph.

Edge clique graphs and some classes of chordal graphs

The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. We describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlike-threshold, split and threshold graphs. In particular, a known necessary condition for a graph to be an edge c...

Edge Clique Covering Sum of Graphs

The edge clique cover sum number (resp. edge clique partition sum number) of a graph G, denoted by scc(G) (resp. scp(G)), is defined as the smallest integer k for which there exists a collection of complete subgraphs of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. By definition, scc(G) 5 scp(G). Also, it is known that for every graph G ...

A Characterization of Edge Clique Graphs

Edge contraction and edge removal on iterated clique graphs

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 dynamical behaviour of a graph under the iteration of the clique operator K. As a consequence of this study, we can now prove the clique divergence of graphs for which no previously known technique would yield the re...