Geodesic
Lexicographic Product of Extendable Graphs
Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Lexicographic product G ο H of two graphs G and H has vertex set V ( G ) × V ( H ) and two vertices ( u 1 , v 1 ) and ( u 2 , v 2 ) are adjacent whenever u 1 u 2 ∈ E ( G ), or u 1 = u 2 and v 1 u 2 ∈ E ( H ). If every matching of G of size k can be extended to a perfect matching in G , then G is called k-extendable . In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the lexicographic product of an m -extendable graph and an n -extendable graph is ( m +1)( n +1)-extendable. In fact, we prove a slightly stronger result.
Classification : 05C70, 05C76. 
@article{BMMS_2010_33_2_a2,
     author = {Bing Bai and Zefang Wu and Xu Yang and Qinglin Yu},
     title = {Lexicographic {Product} of {Extendable} {Graphs}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2010},
     volume = {33},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2010_33_2_a2/}
}
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AU  - Zefang Wu
AU  - Xu Yang
AU  - Qinglin Yu
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Bing Bai; Zefang Wu; Xu Yang; Qinglin Yu. Lexicographic Product of Extendable Graphs. Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2010_33_2_a2/