Certain Product Set Labeling of Graphs and Their Cardinality
Veena Vincent1, Supriya Rajendran2
1Veena Vincent, Department of Mathematics, Amrita Vishwa Vidhyapeetham/ Amrita School of Arts and Sciences/ Kochi, India
2Supriya Rajendran, Department of Mathematics, Amrita Vishwa Vidhyapeetham/ Amrita School of Arts and Sciences/ Kochi, India
Manuscript received on 11 April 2019 | Revised Manuscript received on 16 May 2019 | Manuscript published on 30 May 2019 | PP: 1191-1193 | Volume-8 Issue-1, May 2019 | Retrieval Number: A3421058119/19©BEIESP
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Abstract: A product set-labeling of a graph G is an injective function f: V (G) →P(N) such that the induced edge function f: E(G) →P(N)defined by f*(uv) = f(u)*f(v) is injective. A product set labeling of a graph G is a geometric product set labeling if the set labels of all its elements , that is vertices and edges with respect to the function f are geometric progressions .The number of elements in the set label of a vertex or edge of a graph G is called its cardinality .In this paper , we have found alabeling in which all the edges of a graph G are in geometric progressions even though the set labels of one of its vertex is not a geometric progression. Also the edge cardinalty of such graphs
Index Terms: Edges, Geometric Progressions, Product Set-Labeling, Vertices.
Scope of the Article: Software Product Lines