X− Dominating colour transversals in graphs
DOI:
https://doi.org/10.5269/bspm.v34i2.22997Palabras clave:
X−dominating set, X−dominating colour transversal set, X−chromatic partitionResumen
Let G = (X, Y,E) be a bipartite graph. A X-dominating set D ⊆X is called a X−dominating colour transversal set of a graph G if D is
a transversal of at least one $chi$−partition of G.The minimum cardinal-
ity of a X−dominating colour transversal set is called X−dominating
colour transversal number and is denoted by $chi_{dct}(G)$. We find the
bounds of X−dominating colour transversal number and characterize
the graphs attaining the bound.
Referencias
1. Gera. R, Horton. S and Ramussen. C, Dominator coloring and safe clique Partitions,Congressus Numerantium, Volume 181 (2006),19-32.
2. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in graphs, Marcel Dekker, New York, 1998.
3. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs - Advanced Topics, Marcel Dekker, New York, 1998.
4. Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55; December 1986, 5–14.
5. Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs II, Congressus Numerantium, Volume 64; November 1988, 137-146.
6. V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory of irredundant set, Proyecciones Journal of Mathematics, Volume 30;2011, 19-28.
7. V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory on domination in complement of a graph, International Journal of Computational and Mathematical Sciences, Volume 3;2009, 96-97.
2. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in graphs, Marcel Dekker, New York, 1998.
3. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs - Advanced Topics, Marcel Dekker, New York, 1998.
4. Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs I, Congressus Numerantium, Volume 55; December 1986, 5–14.
5. Stephen Hedetniemi, Renu Laskar, A Bipartite theory of graphs II, Congressus Numerantium, Volume 64; November 1988, 137-146.
6. V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory of irredundant set, Proyecciones Journal of Mathematics, Volume 30;2011, 19-28.
7. V. Swaminathan and Y. B. Venkatakrishnan, Bipartite theory on domination in complement of a graph, International Journal of Computational and Mathematical Sciences, Volume 3;2009, 96-97.
Descargas
Publicado
2015-06-29
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
