In a graph G, let ρ△(G) denote the minimum size of a set of edges and triangles that cover
all edges of G, and let α 1 (G) be the maximum size of an edge set that contains at most one …

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 …

In a graph G, a clique partition of G is a partition P={V1, V2,..., Vq} of V (G) such that the
induced subgraph G [Vi] is a clique (called a clique of P) for each i∈[q]. If a clique partition P …

Let C be a clique covering for E (G) and let v be a vertex of G. The valency of vertex v (with
respect to C), denoted by val C (v), is the number of cliques in C containing v. The local …

Note: An inequality for the line-size sum in a finite linear space Page 1 AUSTRALASIAN
JOURNAL OF COMBINATORICS Volume 68(1) (2017), Pages 118–121 Note: An inequality …

The sigma clique cover number (resp. sigma clique partition number) of graph G, denoted by
scc (G)(resp. scp (G)), is defined as the smallest integer k for which there exists a collection …

A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in
one of these cliques, and the weight of a clique covering is the sum of the sizes of the …

A clique covering of G is defined as a family of cliques of G such that every edge of G lies in
at least one of the cliques. The weight of a clique covering is defined as the sum of the …