ScieXplore: International Journal of Research in Science

P. Hemalatha ¹, V. Nivetha ¹

Affiliations
1 Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamilnadu, IN

Abstract

An F-magic labeling in an F-decomposable graph G of order p and size q is a bijection f :V (G)∪ E(G)→{1,2....p + q} such that for every copy F in the decomposition, Σ_VeV(F)f(v) + Σ_e∈E(F)f(e) is constant. The function f is said to be F-E super magic if f (E(G)) = {1,2,....q}. This article contains, a necessary and some sufficient conditions for some even regular and odd regular graphs G to have an (2k +1) - factor E-super magic decomposition, for k ≥1.

Keywords

F-Decomposable Graph, F-E Super Magic Labeling, (2k + 1)-Factor E-Super Magic Decomposition of Graphs.

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P. Hemalatha ¹, V. Sudha ¹

Affiliations
1 Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamil Nadu, IN

Abstract

The oblong numbers are in the form n(n+1), where n = 1,2, . . . . i.e., the oblong numbers are 2, 6, 12, . . . . If the vertices of the given graph G are labeled with oblong numbers and the edges of the graph are labeled with mean of the labels at the end vertices then G is said to have Oblong Mean Prime Labeling (OMPL). Similarly, if the vertices of G are labeled with oblong numbers and the edges of the graphs are labeled with mean of the absolute difference of the labels at the end vertices then G is said to have Oblong Difference Mean Prime Labeling (ODMPL). In this paper, the Oblong Mean Prime Labeling and Oblong Difference Mean Prime Labeling of Complete Graphs (CGs) K_n, n≥3 and Complete Multipartite Graphs (CMGs), K n n n n i 1 2 t 1 , , , , where 1i t ≤ ≤ have been investigated and obtained the results for such graphs.

Keywords

Complete Graphs (CGs) and Complete Multipartite Graphs (CMGs), Oblong Difference Mean Prime Labeling(ODMPL), Oblong Mean Prime Labeling (OMPL)

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