An acyclic automaton with 6 states and input alphabet a, b is represented below as a

multigraph with the vertices (states) on a horizontal line.

The transition diagram of PSSPM(n) is the edge-labeled directed

multigraph [G.sub.n] = ([V.sub.n], [E.sub.n]) where [V.sub.n] = PSSPM(n) is the set of reachable configurations from the initial configuration ([n.bar]), and [E.sub.n] [subset or equal to] [V.sub.n] x [V.sub.n] x {L, R} such that (a, b, [alpha]) [member of] [E.sub.n] if and only if a [right arrow] b according to PSSPM rules where we choose (recall that there is at most one choice) to apply the [alpha] rule (when there is no choice from a to b, both (a, b, L) and (a, b, R) belong to [E.sub.n]).

Given a commutative C-algebra R, we define an R-weighted planar network of order n to be an acyclic planar directed

multigraph G = (V, E, [omega]), in which 2n distinguished boundary vertices are labeled clockwise as source 1, ..., source n, sink n, ..., sink 1, and the function [omega] : E [right arrow] R associates a weight to each edge.

Definition 3.1 The contact graph of [LAMBDA] is the directed

multigraph [LAMBDA]# with a node for each pseudoline of [LAMBDA] and an arc for each contact of [LAMBDA] oriented from the pseudoline passing above the contact to the pseudoline passing below it.

To such a matrix substitution system we can associate a

multigraph [GAMMA] = (V, E) where the set of vertices is V and we put as many edges from v to w as there are w's in D(v).

We recall that a network is a graph with two distinguished vertices, called poles, such that the

multigraph obtained by adding an edge between the two poles is 2-connected.

elements for [Y.sub.n.m.]) Again, we can regard the problem as an instance of subgraph counts for randomly deleting edges from a given initial graph Fn; in this case taking Fn to be a

multigraph consisting of n double edges.

She later returned to the workforce, becoming the first female Director at Charles Bruning Company/Addressograph

Multigraph Corporation.

constructed a spectral method known as Feature Grouped Spectral

Multigraph (FGSM) which is generated through clustering[26].

When partial volume exists, the algorithm treats the image as a

multigraph and distributes the connectivities in a weighted manner.

Let M be a nonempty set and [??] = (V([??]), Q(G)) be a graph such that V([??]) = M, and B : M [right arrow] P(M) is said to be

multigraph preserving if (g, q) [member of] Q(G), and then (w, p) [member of] Q(G) for all w [member of] Bg and p [member of] Bq.

[6] is a directed

multigraph in which nodes correspond to arrivals/departures at a certain station and at a given time stamp.