Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


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

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


  • M. Ba˘ca, S. Jendrol, M. Miller, and J. Ryan, On irregular total labeling, Discrete Math., 307, (2007), 1378–1388.
  • J. A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin., 18, (2015), 247–252.
  • D. Indriati, Widodo, I. E.Wijayanti, and K. A. Sugeng, On total edge irregularity strength of generalized helm, AKCE Int. J. Graphs and Combin., 10, (2013), 147–155.
  • D. Indriati,Widodo, I. E.Wijayanti, and K. A. Sugeng and M. Ba˘ca, On total edge irregularity strength of generalized web graphs and related graphs, Math. Computer Sc., 9, (2015), 161–167.
  • J. Ivan˘co, and S. Jendrol, The total edge irregularity strength of trees, Discuss. Math. Graph Theory, 26 (2006), 449–456.
  • S. Jendrol, J. Miskuf and R. Sotak, Total edge irregularity strength of complete graphs and complete bipartite graphs, Discrete Maths., 310(3), (2010), 400–407.
  • M V. Modha and K. K. Kanani, K-cordial Labeling of Fan and Double Fan, Int. J. Appl. Math. Res., 2 (2015), 362-369.
  • R. W. Putra and Y. Susanti, On total edge irregularity strength of centralized uniform theta graphs, AKCE Int. J. Graphs and Combin., 15(1) (2018), 7–13.
  • R. W. Putra and Y. Susanti, The total edge irregularity strength of uniform theta graphs, J. Phys.: Conf. Ser., 1097 (2018), 012069.
  • I. Rajasingh and T. Arockiamary, Total edge irregularity strength of subdivided star graph, Triangular Snake, and Ladder, Int. J. Math. Archive, 12, (2016), 39–43.
  • l. Ratnasari and Y. Susanti, Total edge irregularity strength of ladder related graphs, Asian-European J. Maths.,(2018), doi:10.1142/S1793557120500722.
  • W. D. Wallis, Magic Graphs, 2011, Boston: Birkhãuser.
  • E. W. Weisstein, Fan graph, (2008). http://mathworld.wolfram.com/FanGraph.html Accessed 16.08.17.
  • E. W. Weisstein, Parachute graph, (2008). http://mathworld.wolfram.com/ParachuteGraph.html Accessed 16.08.17.

Abstract Views: 361

PDF Views: 1




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

Abstract Views: 361  |  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