New results on vertex equitable labeling

• Main Authors: Pon Jeyanthi, Anthony Maheswari, Mani Vijayalakshmi
• Format: Article
• Language: English
• Published: Yildiz Technical University 2016-05-01
• Series: Journal of Algebra Combinatorics Discrete Structures and Applications
• Online Access: http://dergipark.ulakbim.gov.tr/jacodesmath/article/view/5000184291

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 $A$,  $\left|v_f(a)-v_f(b)\right|\leq1$ and the induced edge labels are $1, 2, 3,\cdots, q$. 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 $S(DA(T_n))$, subdivision of double alternate quadrilateral snake $S(DA(Q_n))$, $DA(Q_m)\odot nK_1$ and $DA(T_m)\odot nK_1$ admit vertex equitable labeling.