The week's pick
Random Articles
Reseach Article
The Minimum Monopoly Distance Energy of a Graph
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 128 - Number 3 |
| Year of Publication: 2015 |
| Authors: Ahmed Mohammed Naji, N.D. Soner |
10.5120/ijca2015906457
|
Ahmed Mohammed Naji, N.D. Soner . The Minimum Monopoly Distance Energy of a Graph. International Journal of Computer Applications. 128, 3 ( October 2015), 1-6. DOI=10.5120/ijca2015906457
Abstract
In a graph G = (V,E), a set M ⊆ V is called a monopoly set of G if every vertex v ∈ V - M has at least d(v)/2 neighbors in M. The monopoly size mo(G) of G is the minimum cardinality of a monopoly set among all monopoly sets in G. In this paper, the minimum monopoly distance energy EMd(G) of a connected graph G is introduced and minimum monopoly distance energies of some standard graphs are computed. Some properties of the characteristic polynomial of the minimum monopoly distance matrix of G are obtained. Finally. Upper and lower bounds for EMd(G) are established.
References
- C. Adiga, A. Bayad, I. Gutman and S.A. Srinivas, The minimum covering energy of a graph, Kragujevac Journal Science, 34(2012), 39-56.
- R. B. Bapat, Graphs and Matrices, Hindustan Book Agency, 2011.
- R. B. Bapat and S. Pati, Energy of a graph is never an odd integer, Bulletin of Kerala Mathematics Association, 1(2011), 129-132.
- E. Berger, Dynamic monopolies of constant size, Journal of Combinatorial Theory, Series B, 83(2001), 191-200.
- J. Bermond, J. Bond, D. Peleg and S. Perennes, The power of small coalitions in graphs, Discrete Applied Mathematics, 127(2003), 399 - 414.
- S. B. Bozkurt, A. D. G¨ung¨or and B. Zhou, Note on the distance energy of graphs, MATCH Communication Mathematical in Computer and Chemistry, 64 (2010), 129-134.
- G. Caporossi, E. Chasset and B. Furtula, Some conjectures and properties on distance energy, Les Cahiers du GERAD, 64 (2009), 1-7.
- P. Flocchini, R. Kralovic, A. Roncato, P. Ruzicka and N. Santoro, On time versus size for monotone dynamic monopolies in regular topologies, Journal of Discrete Algorithms, 1(2003), 129 - 150.
- I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungsz. Graz, 103(1978), 1-22.
- I. Gutman, X. Li, J. Zhang, Graph Energy, (Ed-s: M. Dehmer, F. Em-mert) Streib., Analysis of Complex Networks, From Biology to Linguistics, Wiley-VCH, Weinheim, (2009), 145-174.
- A. D. G¨ung¨or and S. B. Bozkurt, On the distance spectral radius and distance energy of graphs, Linear Multilinear Algebra, 59 (2011), 365-370.
- F. Harary, Graph Theory, Addison Wesley, Massachusetts, 1969.
- G. Indulal, I. Gutman and A. Vijayakumar, On distance energy of graphs, MATCH Communication Mathematical and in Computer Chemistry, 60 (2008), 461-472.
- K. Khoshkhak, M. Nemati, H. Soltani, and M. Zaker, A study of monopoly in graphs, Graph and Combinatorial Mathematics, 29(2013), 1417 - 1427.
- J. H. Koolen and V. Moulton, Maximal energy graphs, Advanced Appllied Mathematics, 26(2001), 47-52.
- X. Li, Y. Shi and I. Gutman, Graph Energy, Springer, New york Heidelberg Dordrecht, London 2012
- A. Mishra and S. B. Rao, Minimum monopoly in regular and tree graphs, Discrete Mathematics, 306(14)(2006), 1586 - 1594.
- D. Peleg, Local majorities; coalitions and monopolies in graphs; a review, Theoretical Computer Science, 282(2002), 231 - 257.
- M. R. Rajesh kanna and B. N. Dharmendra, Minimum covering distance energy of agraph, Applied Mathematical Science, 7 (2013), 5525-5536.
- H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. d. Acharya and h. B. Walikar, Bounds for the distance energy of a graph, Kragujevac Journal of Mathematics, 31 (2008), 59-68.
Index Terms
Keywords