On Graphs with Equal Domination and Chromatic Transversal Domination Numbers
G.Sathiamoorthy1, S.K.Ayyaswamy2, C.Natarajan3

1G.Sathiamoorthy, Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed University Thanjavur, Tamilnadu, India.
2S.K.Ayyaswamy, Department of Mathematics, School of Arts, Sciences and Humanities, SASTRA Deemed Univeristy, Thanjavur, Tamilnadu, India.
3C.Natarajan, Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam, Tamilnadu, India.

Manuscript received on 01 August 2019. | Revised Manuscript received on 07 August 2019. | Manuscript published on 30 September 2019. | PP: 4455-4459 | Volume-8 Issue-3 September 2019 | Retrieval Number: C6801098319/2019©BEIESP | DOI: 10.35940/ijrte.C6801.098319
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: Let χ(G) denote the chromatic number of a graph G = (V,E). A dominating set D ⊆ V(G) is a set such that for every vertex v ∈V(G) D there is at least one neighbor in D. The domination number ϒ(G) is the least cardinality of a dominating set of G. A chromatic transversal dominating set(CTDS) of a graph G is a dominating set D which intersects every color class of each χ-partition of G. The chromatic transversal domination number ϒct(G) is the least cardinality of a CTDS of G. In this paper, we characterize cubic graphs, block graphs and cactus graphs with equal domination number and chromatic transversal domination number.
Keywords— Domination Number, Chromatic Transversal Domination Number, Cubic Graph, Block Graph, Cactus Graph.

Scope of the Article:
Block Chain-Enabled IoT Device and Data Security and Privacy