GRAPH THEORY
Prove/Show that a connected Graph G is not separable if
and only if it is nonseparable.
Definitions for Reference: A connected Graph G is called
nonseparable if it has no cut vertices (A vertex v in a connected
graph G is caled a cut vertex if G-v is disconnected)
A connected graph G is called separable if there exist subgraphs
H1, H2 ⊂ G. with E(H1) ∪ E(H2) = E(G) and E(H1) ∩ E(H2) = ∅. V (H1)...
please prove this problem step by step. thanks
Prove that in every simple graph there is a path from every vertex
of odd degree to some other vertex of odd
degree.
Prove or disprove the following statements.
(a) There is a simple graph with 6 vertices with degree sequence
(3, 3, 5, 5, 5, 5)?
(b) There is a simple graph with 6 vertices with degree sequence
(2, 3, 3, 4, 5, 5)?