For which m and n does the graph Km,n  contain an Euler path? An Euler circuit? Explain.

a) List all the odd vertices of the graph.b) According to Euler’s Theorem, does the graph have an Eulerian circuit? Howdo you know?c) According to Euler’s Theorem, does the graph have an Eulerian path? Howdo you know? What is the difference between a Hamiltonian path and an Eulerian path? A person starting in Columbus must-visit Great Falls, Odessa, andBrownsville (although not necessarily in that order), and then return home toColumbus in one car trip. The road mileage between the cities is shown   Columbus Great Falls Odessa Brownsville Columbus --- 102 79 56 Great Falls 102 --- 47 69 Odessa 79 47 --- 72 Brownsville 56 69 72 --- Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex. Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in…

Complete a path straight at vertex a that ends at vertex c.

Which of the graphs have an Euler tour? * GRAPH A. b h GRAPH B. m Both O Neither O A only B only