Abstract
Let Circ(r, n) be a circular graph. It is well known that its independence number α(Circ(r, n)) = r. In this paper we prove that
for every vertex transitive graph H, and describe the structure of maximum independent sets in Circ(r, n) × H. As consequences, we prove
for G being Kneser graphs, and the graphs defined by permutations and partial permutations, respectively. The structure of maximum independent sets in these direct products is also described.
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The second author is supported by National Natural Foundation of China (Grant No. 10731040) and Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093127110001); the third author is supported by National Natural Foundation of China (Grant No. 11001249) and Zhejiang Innovation Project (Grant No. T200905)
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Geng, X.B., Wang, J. & Zhang, H.J. Structure of independent sets in direct products of some vertex-transitive graphs. Acta. Math. Sin.-English Ser. 28, 697–706 (2012). https://doi.org/10.1007/s10114-011-0311-5
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DOI: https://doi.org/10.1007/s10114-011-0311-5