Delta-Color Complement of a Graph

Let Ģ = (V, E) be a finite, simple colored graph of order n and size m. In this paper, we define δ-color complement and δ^′-color complement of graph as follows. For any two points h and i of Ģ with d(h) = d(i), remove the edge between h and i in Ģ and add the edges of Ģ joining the vertices h and i. Resultant graph is called δ-color complement of Ģ. For any two points h and i of Ģ with d(h) ≠ d(i), delete the edge between h and i in Ģ and add corresponding edge of Ģ between h and i. The graph thus obtained is called δ^′-color complement of Ģ. This paper presents different properties of δ-color and δ^′-color complements, examining their connectivity, self-color complementary, and edge counts in specific graphs.