Local coloring of self complementary graphs. Issue 1 (1st April 2017)

• Record Type: Journal Article
• Authors: Deepa, P.; Srinivasan, P.; Sundarakannan, M.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 14:Issue 1(2017)
• Page Start: 35
• Page End: 41
• Publication Date: 2017-04-01
• Subjects: Coloring -- Local coloring -- Local chromatic number -- Self complementary graph
• DOI: 10.1016/j.akcej.2016.11.005
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: Let G = ( V, E ) be a graph. A local coloring of a graph G of order at least 2 is a function c : V ( G ) ⟶ N having the property that for each set S ⊆ V ( G ) with 2 ≤ | S | ≤ 3, there exist vertices u, v ∈ S such that | c ( u ) − c ( v ) | ≥ m s, where m s is the size of the induced subgraph 〈 S 〉 . The maximum color assigned by a local coloring c to a vertex of G is called the value of c and is denoted by χ ℓ ( c ) . The local chromatic number of G is χ ℓ ( G ) = min { χ ℓ ( c ) }, where the minimum is taken over all local colorings c of G . In this paper we study the local coloring for some self complementary graphs. Also we present a sc-graph with local chromatic number k for any given integer k ≥ 6 .