منابع مشابه
On Hamiltonian Regular Graphs
In this paper we shall determine, when 1 = 6, bounds for numbers f(k, I) and F{k, 1) defined as follows: f{k, l)/F(k, I) is defined to be the smallest integer n for which there exists a regular graph/Hamiltonian regular graph of valency k and girth I having n vertices. The problem of determining minimal regular graphs of given girth was first considered by Tutte [9]. Bounds for f(k, I) have bee...
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In this paper we will consider hamiltonian properties of so-called Toeplitz graphs, which are defined as follows: Definition 1 Let n,m, a1, . . . , am ∈ N, 0 < a1 < · · · < am < n and V := {0, . . . , n− 1}. Define E := {[i, j] ∈ V 2 : ∃k ∈ {1, . . . , m} : |j − i| = ak}. Then the graph (V,E) with set of vertices V and set of edges E is called an undirected Toeplitz graph with entries (or strip...
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We investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices. c © 2002 Elsevier Science B.V. All rights reserved.
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In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as portHamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy...
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We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topolog...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1978
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(78)80009-4