117 research outputs found
Spectral radius and Hamiltonicity of graphs
Let G be a graph of given order and mu(G) be the largest eigenvalue of its
adjacency matrix. We give conditions on mu(G) that imply Hamiltonicity of G and
of its complement
Spectral radius and Hamiltonicity of graphs with large minimum degree
This paper presents sufficient conditions for Hamiltonian paths and cycles in
graphs. Letting denote the spectral radius of the
adjacency matrix of a graph the main results of the paper are:
(1) Let and let be a graph of order ,
with minimum degree If then has a Hamiltonian cycle, unless
or .
(2) Let and let be a graph of
order , with minimum degree If then has a Hamiltonian path, unless
or
In addition, it is shown that in the above statements, the bounds on are
tight within an additive term not exceeding .Comment: 18 pages. This version gives tighter bound
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