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On Total Edge Irregularity Strength of Some Graphs Related to Double Fan Graphs


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1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
     

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Let G = (V(G),E(G)) be a simple, connected, undirected graph with non empty vertex set V(G) and edge set E(G). The function f : V(G) ∪ E(G) ↦ {1,2, ...,k} (for some positive integer k) is called an edge irregular total k−labeling where each two edges ab and cd, having distinct weights, that are f (a)+ f (ab)+ f (b)≠ f (c)+ f (cd)+ f (d). The minimum k for which G has an edge irregular total k−labeling is denoted by tes(G) and called total edge irregularity strength of graph G. In this paper, we determine the exact value of the total edge irregularity strength of double fan ladder graph, centralized double fan graph, and generalized parachute graph with upper path.

Keywords

Total Edge Irregular Strength, Double Fan Graph, Double Fan Ladder Graph, Centralized Double Fan Graph, Generalized Parachute Graph.
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  • On Total Edge Irregularity Strength of Some Graphs Related to Double Fan Graphs

Abstract Views: 36  |  PDF Views: 1

Authors

Husnul Khotimah
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia
Yeni Susanti
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia

Abstract


Let G = (V(G),E(G)) be a simple, connected, undirected graph with non empty vertex set V(G) and edge set E(G). The function f : V(G) ∪ E(G) ↦ {1,2, ...,k} (for some positive integer k) is called an edge irregular total k−labeling where each two edges ab and cd, having distinct weights, that are f (a)+ f (ab)+ f (b)≠ f (c)+ f (cd)+ f (d). The minimum k for which G has an edge irregular total k−labeling is denoted by tes(G) and called total edge irregularity strength of graph G. In this paper, we determine the exact value of the total edge irregularity strength of double fan ladder graph, centralized double fan graph, and generalized parachute graph with upper path.

Keywords


Total Edge Irregular Strength, Double Fan Graph, Double Fan Ladder Graph, Centralized Double Fan Graph, Generalized Parachute Graph.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F24427