Let G = (V, E) be a connected graph
. We define the distance as the minimum length of path connecting vertices u and v in G, denoted by d(u, v).
A connected graph
has excess if it has more edges than vertices.
Let G be a simple connected graph
with vertex set V(G) and edge set E(G).
Furthermore, if each [G.sub.i] with i = 1, 2 is a connected graph
in Definition 4, and the TOE-source [G.sub.1] is a bipartite connected graph
having its own bipartition ([X.sub.1], [Y.sub.1]) and a labelling f satisfying Definition 2, we call the 2-identification graph G = [[circle dot].sub.2] <[G.sub.1], [G.sub.2]> a set-ordered twin odd-elegant graph (So-TOE-graph) and f a set-ordered twin odd-elegant labelling (So-TOE-labelling).
For a connected graph
, the Laplacian matrix L is symmetric and positive semi definite.
They also recognize graphical properties that assuring unique localizability, and proposed an approach G2 to make the two-connected graph localizable and a G3 approach to obtain a trilateration graph based on a connected graph
. These two approaches treat all vertices in the graph as complete, which is more coarse-grained than LAL.
Given a connected graph
G = (V, E) and a positive weight function w defined on E, then any w-minimum cut is a connected sides cut of G.
In this paper, the undirected and connected graph
G will be considered, where its L is positive semidefinite and its eigenvalues are presented by 0 = [[lambda].sub.1] < [[lambda].sub.2] [less than or equal to] ...
We examined both tweets and users in order to create a connected graph
from them with links between user-user, user-tweet and tweet-tweet elements.
All graphs considered in this paper are simple connected graph
without loops and parallel link.
A connected graph
G is said to be double-[psi]-critical if each edge of G is double-[psi]-critical.
This notion does not depend on [x.sub.0], and when (X, d) is a connected graph
with graph distance this notion is equivalent to the transience of the usual random walk on this graph (Proposition 2.2).