In this paper we introduce a new class of digraphs induced by groups. These digraphs can be considered as the generalization of Cayley digraphs. Moreover, various graph properties are expressed in terms of algebraic properties. This did not attract much attention in the literature. Mathematics Subject Classification: 05C25

Suzuki (2004) classified thin weakly distance-regular digraphs and proposed the project to classify weakly distance-regular digraphs of valency 3. The case of girth 2 was classified by the third author (2004) under the assumption of the commutativity. In this paper, we continue this project and classify these digraphs with girth more than 2 and two types of arcs.

In this article we initiate the study of class cover catch digraphs, a special case of intersection digraphs motivated by applications in machine learning and statistical pattern recognition. Our main result is the exact distribution of the domination number for a data-driven model of random interval catch digraphs. c © 2001 Elsevier Science B.V. All rights reserved

‎in this paper we defined the vertex removable cycle in respect of the following‎, ‎if $f$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$g in f $‎, ‎the cycle $c$ in $g$ is called vertex removable if $g-v(c)in in f $.‎ ‎the vertex removable cycles of eulerian graphs are studied‎. ‎we also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎

it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

Regular digraphs of degree d > 1, diameter k > 1 and order N(d, k) = d+· · ·+dk will be called almost Moore (d, k)-digraphs. So far, the problem of their existence has only been solved when d = 2, 3 or k = 2, 3. In this paper we prove that almost Moore digraphs of diameter 4 do not exist for any degree d.

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.

All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are determined. Moreover, all such digraphs are commutative.

We introduce some constructions of weakly distance-regular digraphs of girth 2, and prove that a certain quotient digraph of a commutative weakly distance-transitive digraph of girth 2 is a distancetransitive graph. As an application of the result, we obtain some examples of weakly distanceregular digraphs which are not weakly distance-transitive. Moreover, a class of commutative weakly distanc...

Nonstandard digraphs and transfinite digraphs have been defined and examined in two prior technical reports. The present work examines digraphs that are both nonstandard and transfinite. This requires a combination in certain ways of the techniques used in the prior two works. We first construct herein nonstandard transfinite digraphs for all the naturalnumber ranks. Then, a special kind of non...