Chapter 10: Q1ES (page 738)
How many edges does a \({\rm{50}}\)-regular graph with \({\rm{100}}\)vertices have?
The graph contains \({\rm{2500}}\)edges
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Show that Cnis chromatically 3-critical whenever n is an odd positive integer,\(n \ge 3\)
Show that if the directed graph G is self-converse and H is a directed graph isomorphic to G, then H is also self-converse.
Show that if \({\bf{G}}\) is a simple graph with at least 11 vertices, then either \({\bf{G}}\)or\({\bf{\bar G}}\), the complement of \({\bf{G}}\), is non-planar.
Devise an algorithm for finding the shortest path between two vertices in a simple connected weighted graph that passes through a specified third vertex.
Draw \({K_5}\) on the surface of torus (a doughnut shaped solid) so that no edges cross.
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