Sigma clique covering of graphs

TL;DR

This paper investigates the sigma clique cover and partition numbers of graphs, providing tight bounds and exploring their properties in relation to graph coverings and partitions.

Contribution

It introduces new bounds for sigma clique cover and partition numbers, advancing understanding of clique coverings in graphs.

Findings

Derived tight bounds for scc and scp.

Analyzed properties of sigma clique coverings.

Enhanced theoretical understanding of graph clique partitions.

Abstract

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 of cliques of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. In this paper, among some results we provide some tight bounds for scc and scp.