New results on vertex equitable labeling

The concept of vertex equitable labeling was introduced in [9]. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the induced edge labels are 1; 2; 3; · · · ; q. A graph G is said to be a vertex equitable if it admits a vertex equitable labeling. In this paper, we prove that the graphs, subdivision of double triangular snake S(D(T_n)), subdivision of double quadrilateral snake S(D(Q_n)), subdivision of double alternate triangular snake S(DA(Tn)), subdivision of double alternate quadrilateral snake S(DA(Q_n)), DA(Q_m) ⊙ nK1 and DA(T-m) ⊙ nK1 admit vertex equitable labeling.