(a) Prove by contradiction:
We know the number of edges in a complete graph with n nodes is (because in a complete graph, every node is connected to other n-1 nodes, therefore the degree of every node is (n-1), and the total degree of ...

Solution Summary

Connectedness, Vertices and Edges are investigated. The solution is detiled and well presented.

... the m red and n - m blue vertices.These two ... and blue edges, one of the color components remains connected. ... showing whether one of multiple graphs are connected...

... in G such that removal of all the vertices in S , and all the edges that connect to at least one vertex in S , yields either a non-connected graph or a graph...

... a) Show that if G is a 2-connected graph containing a vertex that is adjacent to at least three vertices of degree 2 ... G) of a graph G is that graph obtained from ...

... Suppose that G is NOT a complete graph. ... Now we consider the remaining vertices of S=V(G)-{u,v}. If ... two edges. So, by the fact that G is connected (as G had ...

... there is a path connecting any two distinct vertices of the ... the graph has only one node, then it is already connected. If n =2 , the graph has two nodes, say u ...

... Part 1. The graph (the first attachment) has 5 vertices, since the ... a Moreover, a vertex i is connected with a vertex j exactly with number ij of ...

... Eulerian graphs are connected, undirected, and their vertices are all of even degree. Observation A: Let n_i denote the number of edges emerging from vertex i ...

... involves the ways in which sets of points, called vertices, can be connected by lines ...Graphs in this context differ from the more familiar coordinate plots ...