Open AccessOn Divisor 3-Equitable Labeling of Wheel Graphs
Author(s) -
K. Tina Jebi Nivathitha*,
N. Srinivasan,
A. Parthiban*,
Mrs. Sangeeta
Publication year - 2020
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.e7040.018520
Subject(s) - combinatorics , mathematics , bijection , graph labeling , graph , divisor (algebraic geometry) , vertex (graph theory) , wheel graph , discrete mathematics , edge graceful labeling , graph power , line graph
A graph on vertices is said to admit a divisor 3- equitable labeling if there exists a bijection ∶ () → {, , . . . , } defined by = = ,()| or |() , = = , and | − | ≤ for all ≤ , ≤ , where denotes the number of edges labelled with “”. A graph which permits a divisor 3-equitable labeling is called a divisor 3-equitable graph. A wheel graph is defined as = −⋀ , where − is a cycle on − vertices and is a complete graph on a single vertex. In this paper, we prove the non-existence of a divisor 3- equitable labeling of the wheel graph for ≥ .