Two construction schemes for cubic hamiltonian 1-node-hamiltonian graphs

Construction schemes for fault-tolerant Hamiltonian graphs

In this paper, we present three construction schemes for fault-tolerant Hamiltonian graphs. We show that applying these construction schemes on fault-tolerant Hamiltonian graphs generates graphs preserving the original Hamiltonicity property. We apply these construction schemes to generate some known families of optimal 1-Hamiltonian graphs in the literature and the Hamiltonicity properties of ...

The domination number of cubic Hamiltonian graphs

Let γ(G) denote the domination number of a graph, and let C be the set of all Hamiltonian cubic graphs. Let γ̄(n) = max {γ(G)| G ∈ C and |V (G)| = n} , and γ(n) = min {γ(G)| G ∈ C and |V (G)| = n} . Then, for n ≥ 4, n even, γ̄(n) = ⌊ n + 1 3 ⌋ and γ(n) = ⌊ n + 2 4 ⌋ .

Hamiltonian decompositions of prisms over cubic graphs

Cubic planar hamiltonian graphs of various types

Let U be the set of cubic planar hamiltonian graphs, A the set of graphs G in U such thatG− v is hamiltonian for any vertex v of G, B the set of graphs G in U such thatG− e is hamiltonian for any edge e of G, and C the set of graphs G in U such that there is a hamiltonian path between any two different vertices of G. With the inclusion and/or exclusion of the sets A,B, and C, U is divided into ...

Hamiltonian Factors in Hamiltonian Graphs

Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor. Keywords—graph, neighborhood, factor, Hamiltonian factor.