Trees, Graphs and Multigraphs - By contracting an edge e = uv, we mean removing e and identifying the vertices u and v as a single new vertex. Let num_T(G) denote the number of spanning trees of the graph G.
a. Show that the follow ...
Trees and Incidence Matrices - Let G be a graph with p vertices and p-1 edges.
Prove that G is a tree iff any p-1 rows of the incidence matrix are linearly independent over Z/(2) (integers modulo 2).
Mean and Standard Deviation - Height of 50 oak trees were measured, but due to problems only partial results were obtained. it was found that 6 trees had a height of less than 9 metres, while 18 trees had a height of less than 15 ...
Directed Graphs and Trees - a. Is a directed graph weakly connected if there is a path from a to b and from b to a
whenever a and b are vertices in the graph?
b. If two trees have the same number of vertices and the same deg ...