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A Study on Edge-Set Graphs of Certain Graphs

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2015
Authors:
Johan Kok, N.K. Sudev, K.P. Chithra
10.5120/ijca2015906385

Johan Kok, N K Sudev and K P Chithra. Article: A Study on Edge-Set Graphs of Certain Graphs. International Journal of Computer Applications 127(6):1-5, October 2015. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {Johan Kok and N.K. Sudev and K.P. Chithra},
	title = {Article: A Study on Edge-Set Graphs of Certain Graphs},
	journal = {International Journal of Computer Applications},
	year = {2015},
	volume = {127},
	number = {6},
	pages = {1-5},
	month = {October},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

Let G(V,E) simple connected graph, with |E| = ε. In this paper, we define an edge-set graph GG constructed from the graph G such that any vertex Vs,i of GG corresponds to the i-th s-element subset of E(G) and any two vertices Vs,i , Vk,m of GG are adjacent if and only if there is at least one edge in the edge-subset corresponding to Vs,i which is adjacent to at least one edge in the edge-subset corresponding to Vk,m where s, k are positive integers. It can be noted that the edge-set graph GG of a graph G is dependent on both the structure of G as well as the number of edges ε.We also discuss the characteristics and properties of the edge-set graphs corresponding to certain standard graphs.

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Keywords

Edge-set graph, Total edge-degree of a graph, Edge-degree of vertex, Connected edge dominating set, Artificial edge-set element