How many different patterns may be formed by coloring the vertices of a regular octagon using c c...
COMP Discrete Structures: Please answer completely and clearly. (3). (5). x) (4 points) If k is a positive integer, a k-coloring of a graph G is an assignment of one of k possible colors to each of the vertices/edges of G so that adjacent vertices/edges have different colors. Draw pictures of each of the following (a) A 4-coloring of the edges of the Petersen graph. (b) A 3-coloring of the vertices of the Petersen graph. (e) A 2-coloring (d) A...
B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V → {0, 1, . . . ,k-1} such that c(u)≠c(v) for every edge (u, v) ∈ E. In other words, the numbers 0.1,... k-1 represent the k colors, and adjacent vertices different colors. must havec. Let d be the maximum degree of any vertex in a graph G. Prove that we can color G with d +1 colors.
how many edges does a 4-regular graph on n on vertices have?
How many different unrooted binary trees on are there on n vertices?
How many distinctly different “words” can be formed using the letters of the word “OTTAWA”?
How many different undirected graphs are possible with the same set of 5 vertices V = {A, B, C, D, E}, but different sets of edges E?
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
If q colors are available, how many ways can a. the vertices of a tetrahedron be painted? b. the edges of a tetrahedron be painted?
014) Draw a dual graph G for the following planar map, and find a coloring for the vertices of G that uses x(G) number of colors o cean Q15. Solve the following TSP problem 3 4 55305 302 320 C Using the nearest neighbor algorithm., if A is the home city. Shade the edges used. Find the distance travelled. E x piaun the qlgor tam a) 340 305 30 D 320 С Using the sorted edge algorithm. Show work (...
(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.