# 图的度和与扩圈Extending Cycles and Degree Sums in Graphs

Abstract: In this paper, we study the relations between degree sums and extending cycles in graphs. The following results is proved. Let G be a graph of order . If for each pair of nonadjacent vertices u,v in , then every cycle C of G with is extendable. By the result,we have that if for each pair of nonadjacent vertices u,v in , then G is fully cycle ex-tendable.

[1] J. A. Bondy，U. S. R. Murty. Graph theory with applications. New York: Macmillan London and Elsevier, 1976.

[2] Ｇ.Ａ. Dirac. Some theorems on abstract graphs. Proceedings London Mathematical Society, 1952, s3-2(1): 69-81.

[3] O. Ore. Note on Hamilton circuits. The American Mathematical Monthly, 1960, 67: 55.

[4] G. R. T. Hendry. Extending cycles in graphs. Discrete Mathematics, 1990, 85(1): 59-72.

Top