Let D(p, q) be a digraph. A function f: V → {1, 2, ..., n} is said to neighborhood prime labeling of D if it both in and out degree labeling. In this paper, we introduce the concept digraphs also investigate existence some digraphs.

From a natural generalization to E* of the concept of congruence, it is possible to define a family of 2-regular digraphs that we call double commutative-step digraphs. They turn out to be Cayley diagrams of Abelian groups generated by two elements, and can be represented by L-shaped tiles which tessellate the plane periodically. A double commutative-step digraph with n vertices is said to be t...

We classify the finite connected-homogeneous digraphs, as well as the infinite locally finite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families ...

Comparisons within monozygotic and dizygotic twin pairs can provide valuable insights into the relative contributions of genetic and environmental influences on the variation in tooth size. Twenty-two twin pairs (12 dizygotic twins, 10 monozygotic twins) aged 13 – 25 years who met the inclusion and exclusion criteria were considered. Mesio-distal measurements of maxillary and mandibular permane...

Domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This thesis focuses on domination theory, and the main aim of the study is to apply a probabilistic approach to obtain new upper bounds for various domination parameters. Chapters 2 and ...

The semigroup DV of digraphs on a set V of n labeled vertices is defined. It is shown that DV is faithfully represented by the semigroup Bn of n × n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in DV follow directly from the Green’s classifications already established for Bn. The new results found from this are: (i) L, R, and H equivalent digraphs...

In this paper we present suucient conditions for unweighted digraphs to induce facet-deening inequalities of the linear ordering polytope P n. We introduce constructive operations (Identiication (of nodes),5-Extension) for generating new facets of P n by using already known facets. The identiication generates new digraphs by identiication two nodes of the source di-graph and presented for arbit...