An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

Let G be a nonsingular connected mixed graph. We determine the mixed graphs G on at least seven vertices with exactly two Laplacian eigenvalues greater than 2. In addition, all mixed graphs G with exactly one Laplacian eigenvalue greater than 2 are also characterized. c © 2006 Elsevier Ltd. All rights reserved.

A mixed graph is a graph with some directed edges and some undirected edges. We introduce the notion of mixed matroids as a generalization of mixed graphs. A mixed matroid can be viewed as an oriented matroid in which the signs over a fixed subset of the ground set have been forgotten. We extend to mixed matroids standard definitions from oriented matroids, establish basic properties, and study...

In a mixed (Δ, d)-regular graph, every vertex is incident with Δ ≥ 1 undirected edges and there are d ≥ 1 directed edges entering and leaving each vertex. If such a mixed graph has diameter 2, then its order cannot exceed (Δ+ d) + d+1. This quantity generalizes the Moore bounds for diameter 2 in the case of undirected graphs (when d = 0) and digraphs (when Δ = 0). For every d such that d − 1 is...

We introduce a new family of mixed graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. Moreover, there can be up to three edges between any pair of nodes. The new family includes Richardson’s acyclic directed mixed graphs, as well as Andersson-Madigan-Perlman chain graphs. These features imply that no family of mixed grap...

We give counterexamples to two conjectures in \Bill Jackson, Some remarks on arc-connectivity, vertex splitting, and orientation in graphs and digraphs, Journal of Graph Theory, 12(3):429{436, 1988" concerning orientations of mixed graphs and splitting oo in digraphs, and prove the rst conjecture in the (di-) Eulerian case(s). Beside that we solve the degree constrained directed augmentation pr...