For each graph below, determine: the vertex set, the edge set, the order, the si
ID: 3143084 • Letter: F
Question
For each graph below, determine: the vertex set, the edge set, the order, the size, the minimum degree, the maximum degree, the total degree, the average degree, and the degree sequence. Answer the following questions about the graph (b) show on the right in the previous problem. (a) Find all edges that are incident on v_1. (b) Find all vertices that are adjacent to v_2. (c) Find all edges that are adjacent to e_2. (d) Find all loops. (e) Find all parallel edges. (f) Find all isolated vertices. (g) Find the degree of v_2.Explanation / Answer
(a) Vertex set={a,b,c,d,e,f,g.h,i}
Edge set={(a,b),(a,i),(i,b),(h,b),(h,i),(h,g)(h,c),(g,c)(g,f),(g,d),(i,f),(f,e),(f,d),(c,d),(e,d),(b,c)}
Order of graph=no. of vertices=9
Size of graph=no. of edges=16
Min degree=2
Max degree=4
Total degree=32
Average degree=4
Degree sequence={2.4,4,4,2,4,4,4,4}
(b) Vertex set={v1,v2,v3,v4,v5}
Edge set={e1,e2,e3,e4,e5,e6,e7}
Order of graph=no. of vertices=5
Size of graph=no.of edges=7
Min degree=0
Max degree=6
Total degree=14
Average degree=2.8
Degree sequence={4,6,2,0,2}
(a) Edges that inciden of V1 are e1,e2,e7
(b) Edgesthat incidenton V2 are e2,e3,e4,e5,e6
(c) v1 and v2
(d) e1,e3
(e) No edges are parallel
(f) v4
(e) degree of v2 is 6
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