Spectral radius and Hamiltonian properties of graphs
Citations
71 citations
45 citations
43 citations
36 citations
34 citations
References
[...]
298 citations
202 citations
"Spectral radius and Hamiltonian pro..." refers background in this paper
...Lemma 6 (Hong et al. [18], Nikiforov [19]) For nonnegative integers p and q with 2q ≤ p(p − 1) and 0 ≤ x ≤ p − 1, the function f (x) = (x − 1)/2+√2q − px + (1+ x)2/4 is decreasing with respect to x....
[...]
...Theorem 3 (Fiedler and Nikiforov [2]) Let G be a graph on n vertices....
[...]
...Nikiforov [19] proved it for general graphs independently, and the case of equality was characterized in [20]....
[...]
...[18], Nikiforov [19]) For nonnegative integers p and q with 2q ≤ p(p − 1) and 0 ≤ x ≤ p − 1, the function f (x) = (x − 1)/2+√2q − px + (1+ x)2/4 is decreasing with respect to x....
[...]
...Corollary 1 (Fiedler and Nikiforov [2]) Let G be a graph on n vertices....
[...]
157 citations
"Spectral radius and Hamiltonian pro..." refers background in this paper
...[18] proved the following spectral inequality for connected graphs....
[...]
...[18], Nikiforov [19]) For nonnegative integers p and q with 2q ≤ p(p − 1) and 0 ≤ x ≤ p − 1, the function f (x) = (x − 1)/2+√2q − px + (1+ x)2/4 is decreasing with respect to x....
[...]