Discussiones Mathematicae Graph Theory 16(2) (1996)
151-155
DOI: https://doi.org/10.7151/dmgt.1030
A NOTE ON STRONG AND CO-STRONG PERFECTNESS OF THE X-JOIN OF GRAPHS
Alina Szelecka Institute of Mathematics, Technical University of
Zielona Góra |
Andrzej Włoch Department of Mathematics, Technical University of
Rzeszów |
Abstract
Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra andD. Basavayya [5]. In this paper we discuss strong perfectness and co-strong perfectness for the generalized composition (the lexicographic product) of graphs named as the X-join of graphs.
Keywords: strongly perfect graphs, co-strongly perfect graphs, the X-join of graphs.
1991 Mathematics Subject Classification: 05C75, 05C60.
References
[1] | C. Berge and P. Duchet, Strongly perfect graphs, Ann. Disc. Math. 21 (1984) 57-61. |
[2] | M. Borowiecki and A. Szelecka, One factorizations of the generalized Cartesian product and of the X-join of regular graphs, Discussiones Mathematicae 13 (1993) 15-19. |
[3] | M. Kwaśnik and A. Szelecka, Strong perfectness of the generalized Cartesian product of graphs, accepted for publication in the special issue of Discrete Math., devoted to the Second Krako w Conference on Graph Theory, Zakopane 1994. |
[4] | E. Mandrescu, Strongly perfect product of graphs, Czech. Math. Journal, 41 (116) (1991) 368-372. |
[5] | G. Ravindra and D. Basavayya, Co-strongly perfect bipartite graphs, Jour. Math. Phy. Sci. 26 (1992) 321-327. |
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