Involve: A Journal of Mathematics
- Volume 2, Number 1 (2009), 95-114.
Hamiltonian labelings of graphs
For a connected graph of order , the detour distance between two vertices and in is the length of a longest path in . A Hamiltonian labeling of is a function such that for every two distinct vertices and of . The value of a Hamiltonian labeling of is the maximum label (functional value) assigned to a vertex of by ; while the Hamiltonian labeling number of is the minimum value of Hamiltonian labelings of . Hamiltonian labeling numbers of some well-known classes of graphs are determined. Sharp upper and lower bounds are established for the Hamiltonian labeling number of a connected graph. The corona of a graph is the graph obtained from by adding exactly one pendant edge at each vertex of . For each integer , let be the set of connected graphs for which there exists a Hamiltonian graph of order such that . It is shown that for each and that both bounds are sharp.
Involve, Volume 2, Number 1 (2009), 95-114.
Received: 21 August 2008
Accepted: 15 November 2008
First available in Project Euclid: 20 December 2017
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Renzema, Willem; Zhang, Ping. Hamiltonian labelings of graphs. Involve 2 (2009), no. 1, 95--114. doi:10.2140/involve.2009.2.95. https://projecteuclid.org/euclid.involve/1513799120