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Research Article

Extended Roman Domination Number of Honeycomb Networks


Author(s): D.Antony Xavier , ChiranjilalKujur
Affiliation: Department of Mathematics,Loyola college,Chennai
Year of Publication: 2014
Source: International Journal of Computing Algorithm
     
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Citation: D.Antony Xavier, ChiranjilalKujur. "Extended Roman Domination Number of Honeycomb Networks." International Journal of Computing Algorithm 3.1 (2014): 68-70.

Abstract:
An extended Roman domination function on a graph G=(V,E) is a function satisfying the conditions that (i) every vertex u for which f(u) is either 0 or 1 is adjacent to at least one vertex v for which f(v) =3,(ii) if u and v are two adjacent vertices and if f(u)=0 then f(v)≠0. The weight of an extended Roman domination function is the value ( ) Σ ( ) The minimum weight of an extended Roman domination function on graph G is called the extended Roman domination number of G, denoted by ( ) . In this paper we study this variant of domination for honeycomb networks.


Keywords Domination, Extended Roman domination, Extended Roman domination number, Honeycomb networks.


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@article{Ext1458967, author = {D.Antony Xavier,ChiranjilalKujur}, title = {Extended Roman Domination Number of Honeycomb Networks}, journal={International Journal of Computing Algorithm}, volume={3}, issue={1}, issn = {2278-2397}, year = {2014}, publisher = {Scholarly Citation Index Analytics-SCIA}

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  • [7] JafariRad.N, “A note on Roman domination in graphs”. UtilitasMathematica 83, 305–312 , 2010.
  • [8] Kämmerling, K., Volkmann, L.,“Roman k-domination in graphs”, J. Korean Math.Soc., 46, 1309–1318, 2009.
  • [9] P.A. Dreyer, Jr., “Applications and Variations of Domination in Graphs”, Ph.D.Thesis, Rutgers University, October 2000.
  • [10] Revelle, C. S., Rosing, K. E., “Defendens imperium romanum: a classical problem in military strategy”, Amer.Math. Monthly, 107(7), 585–594 , 2000.
  • [11] Vladimir Samodivkin,H. AbdollahzadehAhangar, Michael A. Henning, Christian Löwenstein, Yancai Zhao, “Signed Roman domination in graphs”, Journal of Combinatorial Optimization, June 2012.

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