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A note on strong and co-strong perfectness of the X-join of graphs
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 151-155.

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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 
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Szelecka, Alina; Włoch, Andrzej. A note on strong and co-strong perfectness of the X-join of graphs. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 151-155. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a5/

[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.