The specific case where each edge is assigned a unique color (that is, each link belongs to only one SRLG) is strictly equivalent to the

Labeled Graph model considered by Chang and Leu (1997); Wan et al.

Segev, The complexity of bottleneck

labeled graph problems, In Proc.

By taking the edge labels of a sequentially

labeled graph with q edges modulo q, we obviously obtain a harmoniously

labeled graph.

A

labeled graph can be represented as a quadruple g = <V, E, [l.sub.v], [l.sub.E]>, where V is a set of vertices, and E [subset or equal to] V x V is a set of edges.

Definition 1 (

Labeled Graph) A

labeled graph G is a 4-tuple (V, E, 1, B), where V is the vertex set, E [??] V x V is the edge set, and I is the label function that maps a vertex in V or an edge in E to a label in the label set 8, i.e.

Definition 1 (

Labeled Graph) A

labeled graph G is a five element tuple G = {V, E, [[summation].sub.V], [[summation].sub.E], L} where V is a set of vertices and E [subset not equal to] V x V is a set of undirected edges.

The transformation concept that is used for reconfigurable Petri nets is double-pushout approach on directed,

labeled graphs. This approach has been lifted to a categorical framework using a morphism class M, with various instantiations, called M-adhesive high-level replacement (HLR) systems (see [14]).

When they formulated questions, wrote reports and letters, and

labeled graphs, my students gained experience in clarifying and verbalizing their ideas and expressing them effectively in writing; they also got practice in spelling, punctuation, and handwriting.

Throughout this paper rewritings of directed, relational, and

labeled graphs ar discussed.

Let [G.sub.n,k] be the set of

labeled graphs defined from the set M.

The asymptotic number of

labeled graphs with given degree sequences.

Let l [member of] [2, [l.sub.0]] and let S [subset] [C.sub.n,m] denote the set of

labeled graphs in [C.sub.n,m] whose number of blocks of size t is not in the interval (1 [+ or -] [epsilon]) [b.sub.l]n.