06121173

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06121173 Hou, Xin Min A note on $Z_3$-connected graphs with degree sum condition. Acta Math. Sin., Engl. Ser. 28, No. 11, 2161-2168 (2012). 2012 Institute of Mathematics, Academia Sinica, Beijing; Springer, Heidelberg EN group connectivity degree sum condition

doi:10.1007/s10114-012-0710-2

Summary: A graph $G$ satisfies the Ore-condition if $d(x)+d(y) {\ge} |V(G)|$ for any $xy \notin E(G)$. Luo et al. [European J. Combin., 2008 characterized the simple $Z_3$-connected graphs satisfying the Ore-condition. In this paper, we characterize the simple $Z-3$-connected graphs $G$ satisfying $d(x) + d(y) {\ge} |V(G)| - 1$ for any $xy {\in} E(G)$, which improves the results of Luo et al.