Local coloring of self complementary graphs. Issue 1 (1st April 2017) - Deepa, P.; Srinivasan, P.; Sundarakannan, M.
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 .