how many edges does a 4-regular graph on n on vertices have?
It's genral formula is for k - regular graph on n vertices kn/2 .so in our question k =4
Then , 4.n/2=2n vertices
Let G be a connected graph with n vertices and n edges. How many cycles does G have? Explain your answer.
A forest contains 23 vertices and 20 edges. How many connected components does the graph have?
A graph has 4 vertices of degrees 3, 3, 4, 4. (a) How many edges such a graph have? (b) Draw two non isomorphic such graphs. (c) Explain why there is no such simple graph
(7) Sketch any connected 3-regular Graph G with 6 vertices, determine how many edges must be removed to produce a Spanning Tree and then sketch any Spanning Tree.
Problem 1: In the graph below 6 5 4 1 3 (a) How many edges does the graph have? (b) Which vertices are odd, and which vertices are even? (c) is the graph connected? (d) Does the graph have any bridges? If so, list them all.
North Bank South Bank How many vertices are in your graph? How many edges are in your graph? Give the degree of each vertex: deg(A) = , deg(B) = , deg(C) = , deg(North) = deg(South) = Does this graph have an Euler Circuit, an Euler Path, or Neither?
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
Graph theory a) prove that there is a 3 regular graph if n is even and n>=4 b) thank you Exercise 4. How many distinct graphs are there with vertex set {1,2,...,n}? How many distinct graphs are there with vertex set {1,2,...,n} and m edges? For these questions, what happens if "with vertex set {1,2,...,n}" is replaced by "with n vertices"?
Prove that any graph with n vertices and at least n + k edges must have at least k + 1 cycles.
Question 16. A maximal plane graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph. (a) Draw a maximal plane graphs on six vertices. (b) Show that a maximal plane graph on n points has 3n − 6 edges and 2n − 4 faces. (c) A triangulation of an n-gon is a plane graph whose infinite face boundary is a...