In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

In this paper we use the concept of integer-pair sequences, an invariant of graphs and digraphs introduced in Hakimi and Patrinos [9], and results on its unique realizability, in Das [4,5], to obtain results on the unique realizability of degree sequences, another invariant of graphs and digraphs. We thus present a unified approach to solving the problem of unique realizability of these two inv...

The multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dime...

The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232–251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained...

We study the complexity of two dual covering and packing distance-based problems Broadcast Domination Multipacking in digraphs. A dominating broadcast a digraph D is function $$f:V(D)\rightarrow {\mathbb {N}}$$ such that for each vertex v D, there exists t with $$f(t)>0$$ having directed path to length at most f(t). The cost f sum f(v) over all vertices v. multipacking set S every integer d, ar...

Introduction By Ghouila-Houri's theorem [10], every strong digraph of order n and with minimum degree at least n is Hamiltonian. Extensions of this theorem can be found in [11, 13, 16, 18]. Nash-Williams [15] raised the problem of describing all the extreme digraphs for Ghouila-Houri's theorem, i.e. the strong non-Hamiltonian digraphs of order n and minimum degree n — 1. Bondy [4] specialized t...

given a graph $g$, let $g^sigma$ be an oriented graph of $g$ with the orientation $sigma$ and skew-adjacency matrix $s(g^sigma)$. then the spectrum of $s(g^sigma)$ consisting of all the eigenvalues of $s(g^sigma)$ is called the skew-spectrum of $g^sigma$, denoted by $sp(g^sigma)$. the skew energy of the oriented graph $g^sigma$, denoted by $mathcal{e}_s(g^sigma)$, is defined as the sum of the n...

Some partition theorems similar to the Rogers-Ramanujan theorems are proved. We shall prove the following partition theorems, namely THEOREM 1. The number of partitions of k, k = a 1 + a 2 + a 3 + · · · with a 1 > a 2 ≥ a 3 > a 4 ≥ · · ·

In this paper we study the complementarity spectrum of digraphs, with special attention to problem digraph characterization through spectrum. That is, whether two non-isomorphic digraphs same number vertices can have eigenvalues. The eigenvalues matrices, also called Pareto eigenvalues, has led (undirected) graphs and, in particular, undirected these is an open problem. We characterize one and ...

Cycle pre x digraphs are a class of Cayley coset graphs with many remarkable properties such as symmetry large number of nodes for a given degree and diameter simple shortest path routing Hamiltonic ity optimal connectivity and others In this paper we show that the cycle pre x digraphs like the Kautz digraphs contain cycles of all lengths l with l between two and N the order of the digraph exce...