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- Title
ON THE S<sub>3</sub>-MAGIC GRAPHS.
- Authors
C., Anusha; V., Anil Kumar
- Abstract
Let G = (V (G), E(G)) be a finite (p, q) graph and let (A, ∗) be a finite non-abelain group with identity element 1. Let f : E(G) → Nq = {1, 2, . . ., q} and let g : E(G) → A \ {1} be two edge labelings of G such that f is bijective. Using these two labelings f and g we can define another edge labeling ` : E(G) → Nq × A \ {1} by l(e) := (f(e), g(e)) for all e ∈ E(G). Define a relation ≤ on the range of l by: (f(e), g(e)) ≤ (f(e'), g(e')) if and only if f(e) ≤ f(e'). This relation ≤ is a partial order on the range of `. Let {(f(e1), g(e1)),(f(e2), g(e2)), . . .,(f(ek), g(ek))} be a chain in the range of `. We define a product of the elements of this chain as follows: Πi=1k (f(ei), g(ei)) := ((((g(e1) ∗ g(e2)) ∗ g(e3)) ∗ · · ·) ∗ g(ek). Let u ∈ V and let N∗ (u) be the set of all edges incident with u. Note that the restriction of ` on N∗ (u) is a chain, say (f(e1), g(e1)) ≤ (f(e2), g(e2)) ≤ · · · ≤ (f(en), g(en)). We define l*(u):= Π i=1n (f(ei), g(ei)). If l*(u) is a constant, say a for all u ∈ V (G), we say that the graph G is A - magic. The map l* is called an A -magic labeling of G and the corresponding constant a is called the magic constant. In this paper, we consider the permutation group S3 and investigate graphs that are S3-magic.
- Subjects
PERMUTATION groups; FINITE groups; GRAPH labelings; GROUP identity; NONABELIAN groups; MAGIC
- Publication
South East Asian Journal of Mathematics & Mathematical Sciences, 2022, Vol 18, Issue 3, p317
- ISSN
0972-7752
- Publication type
Article
- DOI
10.56827/SEAJMMS.2022.1803.26