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.