if it satisfies
for every pair
of vertices at distance 2, where
}. For a noncomplete graph
, the number
is defined as
, for a complete graph
. In this paper, we prove that a 2-connected
is hamiltonian if
, moreover it is best possible.
Key Words: -dominated graph, quasi claw-free
graph, neighborhood union, hamiltonicity.
2010 Mathematics Subject Classification: Primary 05C45.
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