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**Shin-Shin Kao, Jui-Chia Wu and Yuan-Kang Shih ^{1}
**

Chung Yuan Christian University

Chungli, 320 Taiwan

E-mail: skao@math.cycu.edu.tw

National Chiao Tung University

Hsinchu, 300 Taiwan

In this paper, we discuss many properties of graphs of *Matching Composition Networks*
(*MCN*) [16]. A graph in *MCN* is obtained from the disjoint union of two graphs *G*_{0}
and *G*_{1} by adding a perfect matching between *V*(*G*_{0}) and *V*(*G*_{1}). We prove that any graph
in *MCN* preserves the hamiltonian connectivity or hamiltonian laceability, and pancyclicity
of *G*_{0} and *G*_{1} under simple conditions. In addition, if there exist three internally
vertex-disjoint paths between any pair of distinct vertices in *G _{i}* for

*
Keywords:
*
hypercube-like graphs, perfect matching, hamiltonian-connected, pancyclic,
3*-connected

Retrieve PDF document (**200803_19.pdf**)

Received March 9, 2006; revised June 22, 2006; accepted October 18, 2006.

Communicated by Tsan-sheng Hsu.
^{*} This work was supported in part by the National Science Council of Taiwan, R.O.C., under contract No. NSC
94-2115-M-033-006 and NSC 95-2115-M-033-002.