Local distance antimagic chromatic number for the union of star and double star graphs

Abstract

UDC 519.17 Let G = ( V , E ) be a graph on p vertices with no isolated vertices. A bijection f from V to { 1,2 ,3 , … , p } is called a local distance antimagic labeling if, for any two adjacent vertices u and v , we receive distinct weights (colors), where a vertex x has the weight w ( x ) = ∑ v ϵ N ( x ) f ( v ) . The local distance antimagic chromatic number χ l ⅆ a ( G ) is defined as the least number of colors used in any local distance antimagic labeling of G . We determine the local distance antimagic chromatic number for the disjoint union of t copies of stars and double stars.