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- Title
PD-Divisor Labeling of Graphs.
- Authors
Kasthuri, K.; Karuppasamy, K.; Nagarajan, K.
- Abstract
Let G = (V (G);E(G)) be a simple, finite and undirected graph of order n. Given a bijection f: V (G) → V{1; 2; . . .; |V (G)|}, we associate two integers P = f(u)f(v) and D = jf(u)-f(v)j with every edge uv in E(G). The labeling f induces on edge labeling f0: E(G) → f0; 1g such that for any edge uv in E(G), f0(uv) = 1 if D j P and f'(uv) = 0 if D - P. Let ef' (i) be the number of edges labeled with i ∊ f0; 1g. We say f is an PD-divisor labeling if f0(uv) = 1 for all uv ∊ E(G). Moreover, G is PD-divisor if it admits an PD-divisor labeling. We say f is an PD-divisor cordial labeling if jef0 (0) - ef' (1) ≥ 1. Moreover, G is PD-divisor cordial if it admits an PD-divisor cordial labeling. In this paper, we define PD-divisibility and PD-divisor pair of numbers and establish some of its properties. Also, we are dealing in PD-divisor labeling of some standard graphs.
- Subjects
GRAPH labelings; UNDIRECTED graphs; BIJECTIONS; INTEGERS
- Publication
International Journal of Mathematical Combinatorics, 2023, Vol 3, p95
- ISSN
1937-1055
- Publication type
Article