For a strong oriented graph D of order n and diameter d and an integer k with 1 ≤ k ≤ d, the kth power D of D is that digraph having vertex set V (D) with the property that (u, v) is an arc of D if the directed distance ~ dD(u, v) from u to v in D is at most k. For every strong digraph D of order n ≥ 2 and every integer k ≥ ⌈n/2⌉, the digraph D is Hamiltonian and the lower bound ⌈n/2⌉ is sharp....

This research, works with the effective Hamiltonian and the quark model. Using, the decay rates of matter-antimatter of b quark was investigated. We described the effective Hamiltonian theory which was applied to the calculation of current-current (Q1,2), QCD penguin (Q3,…,6), magnetic dipole (Q8) and electroweak penguin (Q7,…,10) decay rates. The gluonic penguin structure of hadronic decays ...

In this research we work with the effective Hamiltonian and the quark model. We investigate the decay rates of matter-antimatter of quark. We describe the effective Hamiltonian theory and apply this theory to the calculation of current-current ( ), QCD penguin ( ), magnetic dipole ( ) and electroweak penguin ( ) decay rates. The gluonic penguin structure of hadronic decays is studied thro...

A Hamilton cycle is a cycle containing every vertex of a graph. A graph is called Hamiltonian if it contains a Hamilton cycle. The Hamilton cycle problem is to find the sufficient and necessary condition that a graph is Hamiltonian. In this paper, we give out some new kind of definitions of the subgraphs and determine the Hamiltoncity of edges according to the existence of the subgraphs in a gr...

A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can b...

Hamiltonian cycles on planar random lattices are considered. The generating function for the number of Hamiltonian cycles is obtained and its singularity is studied. Hamiltonian cycles have often been used to model collapsed polymer globules[1]. A Hamiltonian cycle of a graph is a closed path which visits each of the vertices once and only once. The number of Hamiltonian cycles on a lattice cor...

A Hamiltonian cycle of a graph G is a cycle which contains all vertices of G. Two Hamiltonian cycles C1 = 〈u0, u1, u2, ..., un−1, u0〉 and C2 = 〈v0, v1, v2, ..., vn−1, v0〉 in G are independent if u0 = v0, ui 6= vi for all 1 ≤ i ≤ n − 1. If any two Hamiltonian cycles of a Hamiltonian cycles set C = {C1, C2, ..., Ck} are independent, we call C is mutually independent. The mutually independent Hami...

An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known...

Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar. Preface Graph theory as a very popular area of discrete mathematics has rapidly been developed over the last couple of decades. Numerous theoretical results and countless applications to practical problems have been discovered. The concepts of k-ordered graphs and out-arc pancyclicity are two recent topics i...