Graph theory Assignment Question
Graph is defined:
G=(V,B), V= {1,2,3,4,5,6}, B={{1,2},{1,3},{1,5},{1,6},{2,3},{3,4},{3,5},{4,5},{5,6}}.
- The environment of graph G vertex Γ(1)=
1) {2,3,4,6}; 2) {3,4,5};3) {3,4};4) {2,4,5,6}; 5) {2,3,4,5,6}; 6) {2,3,5,6}; 7) {2,3,5}; 8) {3,5}.
Solution: ..........
Answer: .....
- The degree of this vertex is equal to:
1) to three; 2) to six; 3) to five; 4) to eight; 5) to two; 6) to one; 7) to four; 8) to zero.
Solution: ..........
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Graphs G_1 and G_2 are defined of their sets of environment vertecies: γ1={Γ(1)={2,6},Γ(2)={1,3},Γ(3)={2},Γ(4)={5,6},Γ(5)={4,6},Γ(6)={1,4,5}}, Γ2={Γ(1)={5},Γ(2)={6},Γ(3)={4},Γ(4)={3,6},Γ(5)={1,6},Γ(6)={2,4,5}}.
- The set of edges of the graph G1∪ G_2 is:
1) {{1,2},{1,5},{1,6},{2,3},{2,6},{3,4},{4,5},{4,6},{5,6}}; 2) {{1,2},{1,5},{1,6},{2,3},{2,6},{3,6},{4,5},{4,6},{5,6}}; 3) {{1,2},{1,6},{2,3},{2,6},{3,4},{4,5},{4,6},{5,6}}; 4) {{1,2},{1,5},{1,6},{2,3},{2,6},{3,4},{3,5},{4,5},{4,6},{5,6}}.
Solution: ..........
Answer: .....
- Graph (G1∪ G2)-3= :
1) {({1,2,4,5,6},{{1,2},{1,5},{1,6},{2,6},{4,5},{4,6},{5,6}})}; 2) {({1,2,4,5,6},{{1,2},{1,5},{1,6},{2,4}{2,6},{4,5},{4,6},{5,6}})}; 3) {({1,5,6},{{1,5},{1,6},{5,6}})}; 4) {({1,2,3,4,5,6},{{1,2},{1,5},{1,6},{2,6},{4,5},{4,6},{5,6}})}.
Solution: ..........
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- How many assigned edges has the graph G=({s,x,r,q}, { {s, x},{x,r} })?
1) no such edges; 2) 6; 3) five; 4) one; 5) four; 6) two; 7) three.
Solution: ..........
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- The diameter of the graph ({x,g,v}, { {x, g},{g,v} }) is equal to:
1) to four; 2) to three; 3) to one; 4) to two; 5) to zero.
Solution: ..........
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- The radius of the graph ({g,v,s,t}, {{g,v},{v,s},{s,t},{v,t}}) is equal to:
1) to four; 2) to two; 3) to one; 4) to zero; 5) to three.
Solution: ..........
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- How many connection points contains the following graph: G=({u,x,z,r}, { {u, x},{x,z}, {z,u}, {z,r} })?
1) five; 2) three; 3) two; 4) no such points; 5) one; 6) four.
Solution: .........
Answer: .....
The graph G1=(V,B1) is defined of its matrices of sets of verticies and edges:
V= {e, l, o, s, t, x}, B1={{e, o}, {l,o}, {o,s}, {o,t}, {o,x}}.
Graphs G2(V,B2) and G3(V,B3) are defined of their adjacency and incidence matrices:
0 0 0 1 0-> 0 0 0 1 0 1-> 0 0 0 0 0 1-> 0 1 0 0 1 0-> 1 0 0 1 0 0-> 0 1 1 0 0 0;
1 1 0 0 0 0 0-> 0 0 1 1 1 0 0-> 0 0 1 0 0 1 0-> 1 0 0 0 0 1 1-> 0 1 0 1 0 0 1-> 0 0 0 0 1 0 0.
- The set of edges of the graph G=(G1 ∪ G2)⊕ G3 is:
1) {{e,o}, {e,t}, {e,x}, {l,s}, {l,x}, {s,t}}; 2) {{e,o}, {e,s}, {l,o}, {l,x}, {s,t}, {s,x}}; 3) {{e,o}, {e,s}, {l,s}, {l,t}, {o,t}, {o,x}}.
Solution: .........
Answer: .....
