Question

G1: I can create a graph given information or rules about vertices and edges. I can give examples of graphs having combinations of various properties and examples of graphs of special (" named”) types. 1. Draw a graph G with • V(G) = {a,b,c,d,e,f}, • deg(d) = 2, • a and f are neighbors, • {b,d} & E(G), G is simple, • K4 is a subgraph of G. 2. Draw the graph C7. 3. Answer each question about the graph H shown below. (a) Is H connected? (b) Is H regular? (c) Find three numbers n such that Kn is a subgraph of H. (d) Are the vertices b and d adjacent? (e) What is the degree of f? Place work in this bor. Continue on back if needed. f h d 8

Answer 1

d o o + ~(G) = {a, b, c, d, e, f? deg (d)=2 (since neighbours of d a and e] ase there is a and fare neighbours, neighbours, since an edge between a and f. {b, d} & E (a) (since there is no edge between b and d) a is simple (since G has no multiple edges and loops) Consider this is a Kq graph LO F in G. ie, Ky is subgraph of a

in 7 equal the graph with 2 ) CA 7 vertices The cycle is called C7 vertices verten has The noi of edges degree a. every no: of and 3) a) His not connected, Since it has two Components. b) > H is not regular. Because verten every of a regular graph has the same degree deg (a)=4 but deg (b) = 3 for eg:

is a c ) n=2, ie Ka H: subgraph of 3 iek, is a a subgraph 2 Of H ie K4 is n=4, a subgraph 9 of H. Vertices b and ہے are adjacent edge between b and do since there is AM e) degree of f=o, since f is f is an isolated verten.