SOME COVERING BY MONOCHROMATIC PATHS CONCEPTS IN GRAPHS

Iwona Włoch (Poland)

Received April 12, 2008

References:

[1] J. I. Brown, K. Dilcher and R. J. Nowakowski, Roots of independence polynomials of well-covered graphs, J. Alg. Combin. 11 (2000), 197-210. [2] O. Favaron and B. L. Hartnell, On well-k-covered graphs, J. Combin. Math. Combin. Comput. 6 (1989), 199-205. [3] H. Galeana-Sanchez, Kernels in edge-coloured digraphs, Discrete Math. 184 (1998), 87-99. [4] M. D. Plummer, Some covering concepts in graphs, J. Combin. Theory 8 (1970), 91-98. [5] J. Topp, Domination, independence and irredundance in graphs, Dissertationes Mathematicae, Warszawa, 1995. [6] J. Topp and L. Volkmann, On the well-coveredness of product of graphs, Ars Combinatoria 33 (1992), 199-215. [7] I. Włoch, Parameters of independence and domination by monochromatic paths of graphs, submitted. [8] I. Włoch, Some operations of graphs that preserve the property of well-covered by monochromatic paths, Australasian J. Combinatorics 40 (2008), 229-236. [9] A. Włoch and I. Włoch, Monochromatic Fibonacci numbers of graphs, Ars Combinatoria 82 (2007), 125-132.

Keywords and phrases: monochromatic paths, independence, well-covered graphs.