On graphs whose chromatic transversal number is two

Ayyaswamy, S. K.; Natarajan, C.

doi:10.4067/s0716-09172011000100006

Cited by 4 publications

(2 citation statements)

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“…Nevertheless, these are not the only examples of such a transversal-type results in the literature (for instance, see [1], for the case of strong partition independence or strong chromatic number to just mention at least two of them). Some other examples (and again not the only ones) are [3,13], connecting transversals with the chromatic number. According to the amount of literature about this topic in every of its related variants, we restrict our references principally to those ones which are only citing papers that we really refer to in a non-superficial way.…”

Section: Introductionmentioning

confidence: 99%

Independent transversal dominating sets in graphs: Complexity and structural properties

Ahangar¹,

Samodivkin²,

Yero³

2016

Filomat

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A dominating set of a graph G which intersects every independent set of maximum cardinality in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γ it (G). In this paper we study some complexity issues on some independent transversal domination related problems. On the other side, we prove that for every integers a, b, c with a ≤ b ≤ a + c, there exists a graph G such that G has domination number a, minimum degree c and independent transversal domination number b. We also give some other properties of independent transversal dominating sets in graphs.

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Section: Introductionmentioning

confidence: 99%

Independent transversal dominating sets in graphs: Complexity and structural properties

Ahangar¹,

Samodivkin²,

Yero³

2016

Filomat

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“…The parameter γ ct for a few well known graphs was computed by L. Benedict et al [8]. S. K. Ayyaswamy et al [2] characterized graphs for which γ ct = 2. (c) If X = P 1 or P 3 , both vertices in N (X) of degree greater than 2 are supports and if X = P 2 , at least one vertex in N (X) of degree greater than 2 is a support.…”

Section: Introductionmentioning

confidence: 99%

On Graphs With Equal Chromatic Transversal Domination and Connected Domination Numbers

Ayyaswamy¹,

Natarajan²,

Venkatakrishnan³

2012

Communications of the Korean Mathematical Society

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Let G = (V, E) be a graph with chromatic number χ(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every χ-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by γct(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

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Global dominating sets in minimum coloring

Hamid¹,

Rajeswari

2014

Discrete Math. Algorithm. Appl.

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In this paper, we introduce the concept of global dominating-χ-coloring of a graph and the corresponding parameter namely global dominating-χ-color number. Let G be a graph. Among all χ-colorings of G, a coloring with the maximum number of color classes that are global dominating sets in G is called a global dominating-χ-coloring of G. The number of color classes that are global dominating sets in a global dominating-χ-coloring of G is defined to be the global dominating-χ-color number of G, denoted by gd χ(G).

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On graphs whose chromatic transversal number is two

Abstract: In this paper we characterize the class of trees, block graphs, cactus graphs and cubic graphs for which the chromatic transversal domination number is equal to two.

Cited by 4 publications

References 1 publication

Independent transversal dominating sets in graphs: Complexity and structural properties

Independent transversal dominating sets in graphs: Complexity and structural properties

On Graphs With Equal Chromatic Transversal Domination and Connected Domination Numbers

Global dominating sets in minimum coloring

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