Graph Theory Worksheet Answers Introduction to Combinatorics and Graph Theory Custom Edition for the University of Victoria Discrete Mathematics Study Guide for MAT212 S Dr Kieka Myndardt
A graph is something that looks like this It has vertices and edges Each edge connects two vertices It is used to model various things where there are connections For example it could be cities and roads between them or it could be the graph of friendship between people each vertex is a person and two people are connected by an 1 Draw Cn for n 0 1 2 3 4 5 Soln These look like loop graphs or bracelets The n 0 graph is empty the n 1 is a single vertex with a loop on it and n 2 is two vertices with a double edge between n 3 is a triangle n 4 is a square etc 2 Is Cn simple Soln For n 3 yes I suppose technically for n 0 too But n 1 has
Graph Theory Worksheet Answers
Graph Theory Worksheet Answers
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Exercises In Graph Theory
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Graph theory studies combinatorial objects called graphs These objects are a good model for many problems in mathematics computer science and engineering Graph theory is not really a theory but a collection of problems Many of those problems have important practical applications and present intriguing intellectual challenges Math 110 Graph Theory Worksheet 4 INSTRUCTIONS You should show all of your work for each problem and always explain your reasoning 1 Sketch a graph which is a tree with 5 vertices that has at least one vertex of degree 3 2 For each of the graphs below determine if the graph is a tree Explain a b c d
Math 111 First Graph Theory Worksheet Names Graph A Graph B Graph C Graph D For Graphs A C and D can you find an Euler Circuit or Euler path label it on the graph if you find one Graph A Graph B Graph C Graph D How many edges does this graph have What is the order of the graph number of vertices Math 110 Graph Theory Worksheet 3 a Draw neatly a complete graph with the ve cities at the vertices and label each edge with the distance between the two cities
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1 Draw Cn for n 0 1 2 3 4 5 2 Is Cn simple 3 Is Cn bipartite 4 Does Cn have an Eulerian circuit How many 5 Does Cn have a Hamiltonian cycle How many 6 Is Cn connected Prove it from the de nition 7 How many walks of length 3 are there in Cn 8 How many paths of length 3 are there 9 How many trails of length 3 are there Math 111 First Graph Theory Worksheet SOLUTIONS Graph A Graph B Graph C Graph D For Graphs A C and D can you find an Euler Circuit or Euler path label it on the graph if you find one Graph A has an Euler path starting and ending vertices are D and E Graph C has an Euler path starting and ending vertices are E and F Graph D does
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