Abstract.
Let G be a graph of order n with connectivity κ≥3 and let α be the independence number of G. Set σ4(G)= min{∑4 i =1 d(x i ):{x 1,x 2,x 3,x 4} is an independent set of G}. In this paper, we will prove that if σ4(G)≥n+2κ, then there exists a longest cycle C of G such that V(G−C) is an independent set of G. Furthermore, if the minimum degree of G is at least α, then G is hamiltonian.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: July 31, 1998¶Final version received: October 4, 2000
Rights and permissions
About this article
Cite this article
Sun, Z., Tian, F. & Wei, B. Degree Sums, Connectivity and Dominating Cycles in Graphs. Graphs Comb 17, 555–564 (2001). https://doi.org/10.1007/PL00013415
Issue Date:
DOI: https://doi.org/10.1007/PL00013415