On Approximating (Connected) 2-Edge Dominating Set by a Tree

2016 ◽  
pp. 161-176
Author(s):  
Toshihiro Fujito ◽  
Tomoaki Shimoda
Keyword(s):  
Dominating Set ◽  
Edge Dominating Set

scholarly journals Connectivity of Semiring Valued Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1227
Author(s):  
Shyam Sundar Santra ◽  
Prabhakaran Victor ◽  
Mahadevan Chandramouleeswaran ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher ◽  
...  
Keyword(s):  
Graph Theory ◽  
Transportation Network ◽  
Dominating Set ◽  
Network Routing ◽  
Graph Connectivity ◽  
Edge Dominating Set

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

scholarly journals New Results on Polynomial Inapproximabilityand Fixed Parameter Approximability of Edge Dominating Set

2014 ◽  
Vol 56 (2) ◽  
pp. 330-346 ◽  
Author(s):  
Bruno Escoffier ◽  
Jérôme Monnot ◽  
Vangelis Th. Paschos ◽  
Mingyu Xiao
Keyword(s):  
Dominating Set ◽  
Edge Dominating Set ◽  
Fixed Parameter

Maximum matching and kernelization of edge dominating set

2018 ◽  
Vol 136 ◽  
pp. 21-24
Author(s):  
Hang Gao ◽  
Wenyu Gao
Keyword(s):  
Dominating Set ◽  
Maximum Matching ◽  
Edge Dominating Set

scholarly journals Approximating edge dominating set in dense graphs

2012 ◽  
Vol 414 (1) ◽  
pp. 92-99 ◽  
Author(s):  
Richard Schmied ◽  
Claus Viehmann
Keyword(s):  
Dominating Set ◽  
Edge Dominating Set ◽  
Dense Graphs

scholarly journals Erratum to: Linear Time Algorithms for Generalized Edge Dominating Set Problems

Algorithmica ◽  
2011 ◽  
Vol 62 (1-2) ◽  
pp. 633-634 ◽  
Author(s):  
André Berger ◽  
Ojas Parekh
Keyword(s):  
Linear Time ◽  
Dominating Set ◽  
Edge Dominating Set ◽  
Linear Time Algorithms

scholarly journals ON SOME BOUNDS OF THE MINIMUM EDGE DOMINATING ENERGY OF A GRAPH

2021 ◽  
Vol 12 (4) ◽  
pp. 1394-1399
Author(s):  
A.Sharmila , Et. al.
Keyword(s):  
Characteristic Polynomial ◽  
Dominating Set ◽  
Simple Graph ◽  
Minimum Cardinality ◽  
Edge Dominating Set ◽  
Eigen Values ◽  
Vertex Set ◽  
G 12

Let G be a simple graph of order n with vertex set V= {v1, v2, ..., vn} and edge set  E = {e1, e2, ..., em}. A subset  of E is called an edge dominating set of G if every edge of  E -  is adjacent to some edge in  .Any edge dominating set with minimum cardinality is called a minimum edge dominating set [2]. Let  be a minimum edge dominating set of a graph G. The minimum edge dominating matrix of G is the m x m matrix defined by G)= , where  = The characteristic polynomial of is denoted by fn (G, ρ) = det (ρI -  (G) ).  The minimum edge dominating eigen values of a graph G are the eigen values of (G).  Minimum edge dominating energy of G is defined as                 (G) =   [12] In this paper we have computed the Minimum Edge Dominating Energy of a graph. Its properties and bounds are discussed. All graphs considered here are simple, finite and undirected.

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