Bandwidth of Graphs Resulting from the Edge Clique Covering Problem

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 ...

Clique Graphs and Edge-clique graphs

Not every edge-clique graph is a clique graph.

Asymptotic Clique Covering Ratios of Distance Graphs

Given a finite set D of positive integers, the distance graph G(Z,D) has Z as the vertex set and {ij : |i−j| ∈ D} as the edge set. Given D, the asymptotic clique covering ratio is defined as S(D) = lim sup n→∞ n cl(n) , where cl(n) is the minimum number of cliques covering any consecutive n vertices of G(Z,D). The parameter S(D) is closely related to the ratio spT(G) χ(G) of a graph G, where χ(...

Edge-Bandwidth of Graphs

The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edgebandwidth is at least as large as bandwidth for every graph, with equality for certain caterpillars. We obtain sharp or nearly sharp bounds on the change in edge-bandwidth under addition, subdivision, or contracti...

Edge covering of acyclic graphs