Statistics

    Map

Twitter

On Edge Dominating Number of Tensor Product of Cycle and Path
( Vol-4,Issue-12,December 2017 )
Author(s):

Robiatul Adawiyah, Darmaji, Reza Ambarwati, Lela Nursafrida, Inge Wiliandani Setya Putri, Ermita Rizki Albirri

Keywords:

edge dominating number, tensor product, path, cycle.

Abstract:

A subset S’ of E(G) is called an edge dominating set ofG if every edge not in S’ is adjacent to some edge in S’. The edge dominatingnumber of G, denoted by γ’(G), of G is the minimum cardinality takenover all edge dominating sets of G. Let G1 (V1, E1) and G2(V2,E2) betwo connected graph. The tensor product of G1 and G2, denoted byG1⨂▒G2 is a graph with the cardinality of vertex |V| = |V1| × |V2|and two vertices (u1,u2) and (v1,v2) in V are adjacent in G1⨂▒G2ifu1 v1 ∈ E1 and u2,v2 ∈E2 . In this paper we study an edge dominatingnumber in the tensor product of path and cycle. The results show thatγ’(Cn⨂▒P2) = ⌈2n/3⌉ for n is odd, γ’(Cn⨂▒P3) = n for n is odd, and theedge dominating number is undefined if n is even. For n ∈even number,we investigated the edge dominating number of its component on tensorproduct of cycle Cn and path. The results are γ’c(Cn⨂▒P2)= ⌈n/3⌉ andγ’c(Cn ⨂▒P3) = ⌈n/2⌉ which Cn ,P2 and P3, respectively, is Cycle order n,Path order 2 and Path order 3.

ijaers doi crossref DOI:

10.22161/ijaers.4.12.6

Paper Statistics:
  • Total View : 132
  • Downloads : 12
  • Page No: 033-036
Cite this Article:
Show All (MLA | APA | Chicago | Harvard | IEEE | Bibtex)
Share:
References:

[1] Arumugam,S., and Vellamal,S. (1998). Edge Domination In Graph, Taiwanese Journal of Mathematics vol.2(2) pp.173-179.
[2] Chemcan, A. (2010). The Edge Domination Number of Connected Graphs. Australasian Journal of Combinatorics vol.48, 185-189.
[3] Gross,L., Jonathan, Yellen, and Jay. (2006). Graph Theory and It’s Application. United State Of America : Chapman and Hall CRC.
[4] Hedetniemi,S. T., dan Mitchell, S. Edge Domination in Graphs. Congr Numer 19, 1977, pp. 489-509.
[5] S.R.Jayaram. (1987) Line Domination in Graph. Graphs Combin vol 3 pp. 357-363.
[6] V.R. Kulli. The Middle Edge Domination in Graph. J Computer and Mathematical Sciences vol.4, 2013, pp. 372-375.
[7] V.R. Kulli. (2012). Inverse Total Edge Domination in Graph, In advances in Domination Theory I, V.R. Kulli ed. Vishwa Intenational Publication Gulbarga India pp. 35-44.
[8] V.R. Kulli. (2012). The Edge Dominating Graph of a Graph, In advances in Domination Theory I, V.R. Kulli ed. Vishwa Intenational Publication Gulbarga India pp. 127-131.
[9] V.R. Kulli.(2013)The Semientire Edge Dominating Graph. Ultra Scientist vol.25(3) A, 2013, pp. 431-434.
[10] V.R. Kulli.(2015) The Neighborhood Total Edge Domination Number of A Graph. International Research Journal of Pure Algebra vol.5(3) A, pp 26-30.