We consider 2-colored digraphs of the primitive ministrong digraphs having given exponents. In this paper we give bounds for 2-exponents of primitive extremal ministrong digraphs.

We construct a family of Cayley digraphs of degree d, diameter k and order kbd/2ck for any d ≥ 4 and k ≥ 3. We also present a collection of bipartite Cayley digraphs of order at least (k − 1)bd/2ck−1 for any degree d ≥ 4 and diameter k ≥ 4. For sufficiently large d and k, our digraphs are the largest known Cayley digraphs of degree d and diameter k, where k 6= d − 1 or d, and our bipartite digr...

Aharoni, R. and I. Ben-Arroyo Hartman, On Greene-Kleitman’s theorem for general digraphs, Discrete Mathematics 120 (1993) 13-24. Linial conjectured that Greene-Kleitman’s theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and exte...

A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphsMCK(d, ) and it is derived from the Kautz...

Iterated line digraphs arise naturally in designing fault tolerant systems. Diameter vulnerability measures the increase in diameter of a digraph when some of its vertices or arcs fail. Thus, the study of diameter vulnerability is a suitable approach to the fault tolerance of a network. In this article we present some upper bounds for diameter vulnerability of iterated line digraphs LkG. Our bo...

The nonexistence of digraphs with order equal to the Moore bound Md;k = 1+d+: : :+d k for d; k > 1 has lead to the study of the problem of the existence ofàlmost' Moore digraphs, namely digraphs with order close to the Moore bound. In 1], it was shown that almost Moore digraphs of order Md;k ? 1, degree d, diameter k (d; k 3) contain either no cycle of length k or exactly one such cycle. In thi...

We give a decomposition formula for the characteristic polynomials of ramified uniform covers of digraphs. Similarly, we obtain a decomposition formula for the characteristic polynomials of ramified regular covers of digraphs. As applications, we establish decomposition formulas for the characteristic polynomials of branched covers of digraphs and the zeta functions of ramified covers of digraphs.

The principle of inclusion-exclusion is specialized in order to count labeled digraphs with separately speciied out-components, in-components, and isolated components. Applications include counting digraphs with no in-nodes or out-nodes, digraphs with a source and a sink, and digraphs with a unique source and a unique sink.

We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ symmetric subset $S$. then focus on family of unitary $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity. show under mild conditions, $\{G_R, G_R^+\}$ pairs integral non-isospectral (generically connected non-bipartite). Then, we obtain conditions such \bar G_R\}$ graphs. Finall...