Abstract
The split graph K rVK s on r+s vertices is denoted by S r,s. A graphic sequence π = (d 1, d 2, ···, d n) is said to be potentially S r,s-graphic if there is a realization of π containing S r,s as a subgraph. In this paper, a simple sufficient condition for π to be potentially S r,s-graphic is obtained, which extends an analogous condition for p to be potentially K r+1-graphic due to Yin and Li (Discrete Math. 301 (2005) 218–227). As an application of this condition, we further determine the values of σ(S r,s, n) for n ≥ 3r + 3s - 1.
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Supported by the National Natural Science Foundation of China (No. 11561017), Natural Science Foundation of Guangxi Province (No. 2014GXNSFAA118361) and Natural Science Foundation of Hainan Province (No. 2016CXTD004).
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Yin, Jh., Meng, L. & Yin, MX. Graphic sequences and split graphs. Acta Math. Appl. Sin. Engl. Ser. 32, 1005–1014 (2016). https://doi.org/10.1007/s10255-016-0622-5
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DOI: https://doi.org/10.1007/s10255-016-0622-5