Hyper-Hamiltonian circulants

Hyper-Hamiltonian generalized Petersen graphs

Assume that n and k are positive integers with n ≥ 2k + 1. A non-hamiltonian graph G is hypo hamiltonian if G − v is hamiltonian for any v ∈ V (G). It is proved that the generalized Petersen graph P (n, k) is hypo hamiltonian if and only if k = 2 and n ≡ 5 (mod 6). Similarly, a hamiltonian graph G is hyper hamiltonian if G−v is hamiltonian for any v ∈ V (G). In this paper, we will give some nec...

Unimodular integer circulants

We study families of integer circulant matrices and methods for determining which are unimodular. This problem arises in the study of cyclically presented groups, and leads to the following problem concerning polynomials with integer coefficients: given a polynomial f(x) ∈ Z[x], determine all those n ∈ N such that Res(f(x), xn − 1) = ±1. In this paper we describe methods for resolving this prob...

Line Graphs and Circulants

The line graph of G, denoted L(G), is the graph with vertex set E(G), where vertices x and y are adjacent in L(G) iff edges x and y share a common vertex in G. In this paper, we determine all graphs G for which L(G) is a circulant graph. We will prove that if L(G) is a circulant, then G must be one of three graphs: the complete graph K4, the cycle Cn, or the complete bipartite graph Ka,b, for s...

Revisiting Hamiltonian De omposition of the Hyper ube

Hyper hamiltonian laceability on edge fault star graph

The star graph possess many nice topological properties. Edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes. In this paper, we show that the n-dimensional star graph is (n 3)-edge fault tolerant hamiltonian laceable, (n 3)-edge fault tolerant strongly hamiltonian laceable, and (n 4)edge fault tolerant hyper hamiltonian laceable. All these ...