E-Cordial Labeling for Theta Graph

Abstract

 A binary vertex labeling  f : E(G) → {0,1} with induced labeling  f ^* : V(G) → {0,1} defined by   f ^*(v) = ∑ { f (uv) : uv ϵ E(G)}(mod 2) is called an E-cordial labeling of  graph G if the number of vertices labeled 0 and number of vertices labeled 1 differ by at most 1and the number of edges labeled 0 and number of edges labeled 1 differ by at most 1.  A graph which admits E-cordial labeling is called an E-cordial graph. We prove that the graphs obtained by duplication, switching, fusion and open star of theta graph T_α are E-cordial graphs.