The hamiltonian numbers in digraphs

Ting-Pang Chang and Li-Da Tong ()
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Ting-Pang Chang: National Sun Yat-sen University
Li-Da Tong: National Sun Yat-sen University

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 16, 694-701

Abstract: Abstract In the paper, we study the hamiltonian numbers in digraphs. A hamiltonian walk of a digraph D is a closed spanning directed walk with minimum length in D. The length of a hamiltonian walk of a digraph D is called the hamiltonian number of D, denoted h(D). We prove that if a digraph D of order n is strongly connected, then $n\leq h(D)\leq\lfloor\frac{(n+1)^{2}}{4} \rfloor$ , and hence characterize the strongly connected digraphs of order n with hamiltonian number $\lfloor\frac{(n+1)^{2}}{4} \rfloor$ . In addition, we show that for each k with $4\leq n\leq k\leq\lfloor \frac{(n+1)^{2}}{4} \rfloor$ , there exists a digraph with order n and hamiltonian number k. Furthermore, we also study the hamiltonian spectra of graphs.

Keywords: Hamiltonian number; Orientation; Hamiltonian spectrum (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-012-9512-9

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