On strong (weak) independent sets and vertex coverings of a graph

Kamath, S. S.; Bhat, Radhakrishna

doi:10.1016/j.disc.2006.07.040

Cited by 13 publications

(7 citation statements)

References 5 publications

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“…Babak and Pooya characterized minimum vertex cover in generalized Petersen graphs [2] and Madhavi and Maheswari obtained exact values of minimum vertex cover and minimum edge cover in Mangoldt graphs [[0]. Various graph characterizations have been done on covering relating to domination parameters [3,9] and matching numbers and new graph parameters such as strong vertex cover, weak and balanced vertex covers [11] and disjoint vertex cover [6] are being defined. Three different distributed vertex cover approximation algorithms were designed in [12].…”

Section: [Ntroductionmentioning

confidence: 99%

Structural analysis of invertible graphs

Amutha

Angel

2015

2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO)

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Reliability is an important issue in systems architecture. This paper focuses on a new class of invertible networks which are more reliable in the sense that if there is a failure in the physical components of the system then there always exists an alternate set of nodes to carry out the job in the complement. A graph G is said to be invertible if there exists an inverse vertex cover in G. The contribution of this paper is a new algorithm for recognizing invertible graphs. Our algorithm runs in linear time and is computationally very simple. We present a characterization for invertible graphs in terms of the breadth first search tree and thereby study their theoretical properties.

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Section: [Ntroductionmentioning

confidence: 99%

Structural analysis of invertible graphs

Amutha

Angel

2015

2015 IEEE 9th International Conference on Intelligent Systems and Control (ISCO)

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“…For an edge x = uv, v weakly covers the edge x if deg(v) ≤ deg(u) in G. A set S ⊆ V is a weak vertex cover [W V C] if every edge in G is weakly covered by some vertex in S. The weak vertex covering number is the minimum cardinality of a W V C denoted by wβ(G). One can easily note that a vertex v ∈ V is balanced if, and only if, deg(v) < deg(u) and deg(v) > deg(w) for some u, w adjacent to v. If a balanced vertex set S ⊆ V covers all the edges of G then S is called a balanced vertex cover [BV C] denoted by Bβ(G) [8].…”

Section: Strong Weak and Balanced Vertex Coversmentioning

confidence: 99%

A STUDY ON THE COVERING NUMBER OF GENERALIZED JAHANGIR GRAPHS $J_{s,m}$

Angel¹,

Amutha²

2013

Int. J. of Pure and Appl. Math.

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A set S of vertices of a graph G = (V, E) is called a vertex cover, if each edge in E has at least one end point in S and the minimum cardinality taken over all vertex covering sets of G is called the covering number of G denoted by β(G). In this paper, we study some results on vertex covering, edge covering, strong and weak covering, and inverse covering numbers denoted by β(G), β ′ (G), sβ(G), wβ(G), β −1 (G) respectively for generalized Jahangir graphs J s,m . We have also characterized the graphs which are invertible.

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“…The strong domination is later studied in (Rautenbach , 1998 ;Hattingh et al, 1998;Henning , 1998). Similar to strong (weak) domination S. S. Kamath and R. S. Bhat (Kamath, 2007) studied strong (weak) independent sets. A vertex ∈ is a cutvertex if − is disconnected.…”

Section: Introductionmentioning

confidence: 99%

The Strong (Weak) Vv-Dominating Set of a Graph

Udupa

Bhat

2019

MJS

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Two vertices , ∈ vv-dominate each other if they incident on the same block. A vertex ∈ strongly vv-dominates a vertex ∈ if u and w, vv-dominate each other and () ≥ (). A set of vertices is said to be strong vv-dominating set if each vertex outside the set is strongly vv-dominated by at least one vertex inside the set. The strong vv-domination number γ () is the order of the minimum strong vv-dominating set of G. Similarly weak vvdomination number γ () is defined. We investigate some relationship between these parameters and obtain Gallai's theorem type results. Several upper and lower bounds are established. In addition, we characterize the graphs attaining some of these bounds.

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On strong (weak) independent sets and vertex coverings of a graph

Cited by 13 publications

References 5 publications

Structural analysis of invertible graphs

Structural analysis of invertible graphs

A STUDY ON THE COVERING NUMBER OF GENERALIZED JAHANGIR GRAPHS $J_{s,m}$

The Strong (Weak) Vv-Dominating Set of a Graph

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