On Lucky Edge Labeling of Splitting Graphs and Snake Graphs
A. Shalini Rajendra Babu1, Ramya N2, Rangarajan K3
1A.Shalini Rajendra Babu, Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai (Tamil Nadu), India.
2Ramya N, Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai (Tamil Nadu), India.
3Rangarajan K, Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai (Tamil Nadu), India.
Manuscript received on 07 March 2019 | Revised Manuscript received on 20 March 2019 | Manuscript published on 30 March 2019 | PP: 638-641 | Volume-8 Issue-5, March 2019 | Retrieval Number: E3299038519/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let Gbe a simple graph with vertex set V(G) and Edge set E(G) respectively. Vertex set V(G) is labeled arbitrary by positive integers and let E(e) denote the edge label such that it is the sum of labels of vertices incident with edge e. The Labeling is said to be lucky edge of labeling if the edge set E(G) is a proper colouring of G, that is if we have E(e1 ) ≠E(e2 ) whenever e1 , and e2 are adjacent edges. The least integer k for which a graph G has a lucky edge labeling from the set {1,2. . .k} is the lucky number of G denoted by η(G). In this paper Lucky edge labeling of Splitting graph, and Snake graphs has shown.
Keyword: Lucky Edge Labeling, Lucky Number, Splitting Graph, Alternate Triangular Snake, Alternate Quadrilateral Snake, Double Alternate Triangular Snake.
Scope of the Article: Cryptography and Applied Mathematics