The degree sequence [pi] = ([a.sub.1],..., [a.sub.k]; [b.sub.1],..., [b.sub.l]) is a bigraphic sequence if there exists a simple bipartite graph G = G(A, B) with [absolute value of A] = k, [absolute value of B] = l realizing [pi] such that the degrees of

vertices in A are [a.sub.1],..., [a.sub.k], and the degrees of the

vertices of B are [b.sub.1],..., [b.sub.l].

We propose to measure the similarity of characters by network characteristics to conduct character correction by

vertices merging with computing structure error of networks.

An L(2,1)-coloring of a graph G is reducible if there exists another L(2,1)-coloring g of G such that G(u) [less than or equal to] f(u) for all

vertices u in G and there exists a vertex v in G such that g(v) < /(v).

Hamiltonian cycle is a cycle connecting all the

vertices in a given graph only once.

However, some important properties in Koch networks, such as vertex labeling, the shortest path routing algorithm, the length of the shortest path between arbitrary two

vertices, the betweenness centrality, and the current and voltage properties of Koch resistor networks have not yet been researched.

For two

vertices u and v of G, the resistance distance between u and v is defined to be the effective resistance between them when unit resistors are placed on every edge of G.

A region-based tamper detection algorithm can only locate a suspicious region with some unaltered

vertices inside that region; however, even with a region-based method, the topological relationship can be considered.

For k-power domination, we define iteratively a set [P.sub.G,k] (S) of

vertices monitored by an initial set S (of PMU).

For a vertex v of graph G = (V, E), [N.sub.G](v) denotes the set of

vertices which are adjacent to v and [d.sub.G](v) = |NG(v)| is called the degree of vertex v.

The solved node voltage sequence (NVS) is used to determine correspondence

vertices of two isomorphism identification kinematic chains.

Let G be a graph with p

vertices and q edges and (Eq.) vertex labeling (Eq.) induces.

A network is represented by a graph (G, V, E) with a set V of

vertices often labelled 1, 2, ..., n and an edge-set E of pairs of distinct

vertices describing an adjacency relation.