塔形图——汉密顿图的一种扩展图

Tower Graph——A Kind of Extended Hamiltonian Graph

提出了一种塔形图 ,它是汉密顿图的扩展。这种塔形图有 m层 ,每层之间有 n个柱子等距支撑 ,节点数为 2 m n- n+ 1。由以色列著名数学家汉密顿爵士在 1895年首次提出的具有 2 0个节点的汉密顿图是塔形图的一个特例。文中研究了这种塔形图的汉密顿图性质 ,给出了这一类图的标准汉密顿圈的构造法 ,并利用作者编制的程序给出了两种典型的塔形图的多种不同的汉密顿圈解。

A kind of extended Hamiltonian graphs, called tower graphs, is presented and its Hamiltonian characteristic is studied. The tower graph consists of m layers and it is supported by n pillars between layers. The Hamiltonian graph first posed by the famous Irish mathematician Sir Willian Rowan Hamilton in 1895, is a special example of tower graph. A standard method for constructing the Hamiltonian circuits in tower graphs is given and the multi solutions of the Hamiltonian circuits for two typical tower graphs are found by the program developed by this paper.