Distance magic labelling of Mycielskian graphs

Pawar, Ravindra Kuber (Department of Mathematics BITS Pilani K K Birla Goa Campus, Goa, India.)
Singh, Tarkeshwar (Department of Mathematics BITS Pilani K K Birla Goa Campus, Goa, India.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications

A graph G = (V, E), where |V(G)| = n and |E(G)| = m is said to be a distance magic graph if there is a bijection f : V(G)→{1, 2, …, n} such that the vertex weight w(u)=∑v ∈ N(u)f(v)=k is constant and independent of u, where N(u) is an open neighborhood of the vertex u. The constant k is called a distance magic constant, the function f is called a distance magic labeling of the graph G and the graph which admits such a labeling is called a distance magic graph. In this paper, we present some results on distance magic labeling of Mycielskian graphs.