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Graph and Network Theory
Math 137A
HOMEWORK 5
(1) Compute the total resistance between u and v in the electrical network of resistors shown below, where one diagonal resistor is two ohms, the other diagonal resistor is three ohms, and the remaining resistors are one ohm.
(2) Find a minimal cost spanning tree using both Kruskal’s and Prim’s algorithms.
(3) Prove, directly from the definition, that every subgraph of a bipartite graph is also bipartite.2
(4) Determine whether the given graph is Eulerian. If it is, find an Eulerian circuit. If it is not, prove it is not.
(5) Determine whether the given graph is Hamiltonian. If it is, find a Hamiltonian cycle. If it is not, prove it is not.
