On Equitable Irregular Graphs
P. Sanakara Narayanan1, S. Saravana Kumar2
1P. Sankara Narayanan, Department of Mathematics, Kalasalingam Academy of Research and Education College, Krishnankoil (Tamil Nadu), India.
2S. Saravana Kumar, Department of Mathematics, KalasalingamAcademy of Research and Education College, Krishnankoil (Tamil Nadu), India.
Manuscript received on 08 January 2020 | Revised Manuscript received on 30 January 2020 | Manuscript Published on 04 February 2020 | PP: 122-124 | Volume-8 Issue-4S4 December 2019 | Retrieval Number: D10441284S419/2019©BEIESP | DOI: 10.35940/ijrte.D1044.1284S419
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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: An k−edge-weighting of a graph G = (V,E) is a map 𝝋: 𝑬(𝑮) → {𝟏,𝟐,𝟑, . . . 𝒌}, }where 𝒌 ≥ 𝟏 is an integer. Denote 𝑺𝝋(𝒗) is the sum of edge-weights appearing on the edges incident at the vertex v under𝝋 . An k-edge -weighting of G is equitable irregular if |𝑺𝝋(𝒖) − 𝑺𝝋(𝒗)| ≤ 𝟏, for every pair of adjacent vertices u and v in G. The equitable irregular strength 𝑺𝒆 (𝑮) of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G. In this paper, we discuss the equitable irregular edge-weighting for some classes of graphs.
Keywords: Edge-Weighting, Equitable Irregular Graphs.
Scope of the Article: Cryptography and Applied Mathematics