A graph consists of nodes and edges. An edge is an (unordered)
pair of two distinct nodes in the graph. We create a new empty
graph from the class Graph. We use the add_node method to add a
single node and the add_nodes method to add multiple nodes. Nodes
are identified by unique symbols. We call add_edge with two nodes
to add an edge between a pair of nodes belonging to the graph. We
can also ask a graph for...
A graph consists of nodes and edges. An edge is an (unordered)
pair of two distinct nodes in the graph. We create a new empty
graph from the class Graph. We use the add_node method to add a
single node and the add_nodes method to add multiple nodes. Nodes
are identified by unique symbols. We call add_edge with two nodes
to add an edge between a pair of nodes belonging to the graph. We
can also ask a graph for...
Prove or disprove: If G = (V; E) is an undirected graph where
every vertex has degree at least 4 and u is in V , then there are
at least 64 distinct paths in G that start at u.
Question 1
a) Prove that if u and v are distinct vertices of a graph G,
there exists a walk from u to v if and only if there exists a path
(a walk with distinct vertices) from u to v.
b) Prove that a graph is bipartite if and only if it contains no
cycles of odd length.
Please write legibly with step by step details. Many thanks!
Suppose G is a connected cubic graph (regular of degree 3) and e
is an edge such that G − e has two connected components G1 and
G2
(a) Explain what connected means.
(b) We say that e is a____________ of G
(c) show that G1 has an odd number of vertices.
(d) draw a connected cubic graph G with an edge e as above.