Finite Simple Undirected Graph Foundations

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

Yes

Undirected edges ignore endpoint order. The answer is Yes; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

Yes

Undirected edges ignore endpoint order. The answer is Yes; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

Yes

Undirected edges ignore endpoint order. The answer is Yes; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

Yes

Undirected edges ignore endpoint order. The answer is Yes; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

No

Undirected edges ignore endpoint order. The answer is No; equal endpoints or endpoints outside V cannot give an edge of this simple graph.

∅

Find distinct neighbors using the explicit edge set: N(0)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{-10, -8}

Find distinct neighbors using the explicit edge set: N(-9)={-10, -8}. Do not infer adjacency from a sketch or drawn-line crossings.

{-10}

Find distinct neighbors using the explicit edge set: N(-7)={-10}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(-5)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(-6)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{-7, -6, -4}

Find distinct neighbors using the explicit edge set: N(-5)={-7, -6, -4}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(-4)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{-4, -2}

Find distinct neighbors using the explicit edge set: N(-3)={-4, -2}. Do not infer adjacency from a sketch or drawn-line crossings.

{-3}

Find distinct neighbors using the explicit edge set: N(-4)={-3}. Do not infer adjacency from a sketch or drawn-line crossings.

{-3, -2}

Find distinct neighbors using the explicit edge set: N(-1)={-3, -2}. Do not infer adjacency from a sketch or drawn-line crossings.

{-2}

Find distinct neighbors using the explicit edge set: N(-1)={-2}. Do not infer adjacency from a sketch or drawn-line crossings.

{0, 1, 2, 3, 4}

Find distinct neighbors using the explicit edge set: N(-1)={0, 1, 2, 3, 4}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(1)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{2, 4}

Find distinct neighbors using the explicit edge set: N(3)={2, 4}. Do not infer adjacency from a sketch or drawn-line crossings.

{3, 4, 5}

Find distinct neighbors using the explicit edge set: N(2)={3, 4, 5}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(7)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(6)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{5, 6, 8}

Find distinct neighbors using the explicit edge set: N(7)={5, 6, 8}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(10)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

{8, 10}

Find distinct neighbors using the explicit edge set: N(9)={8, 10}. Do not infer adjacency from a sketch or drawn-line crossings.

{9}

Find distinct neighbors using the explicit edge set: N(8)={9}. Do not infer adjacency from a sketch or drawn-line crossings.

{9, 10}

Find distinct neighbors using the explicit edge set: N(11)={9, 10}. Do not infer adjacency from a sketch or drawn-line crossings.

{12}

Find distinct neighbors using the explicit edge set: N(13)={12}. Do not infer adjacency from a sketch or drawn-line crossings.

{12, 13, 14, 15, 16}

Find distinct neighbors using the explicit edge set: N(11)={12, 13, 14, 15, 16}. Do not infer adjacency from a sketch or drawn-line crossings.

∅

Find distinct neighbors using the explicit edge set: N(13)=∅. Do not infer adjacency from a sketch or drawn-line crossings.

0

Count distinct neighbors from the explicit edge set to obtain deg(0)=0. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(-9)=2. An isolated vertex has degree zero.

1

Count distinct neighbors from the explicit edge set to obtain deg(-7)=1. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(-5)=0. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(-6)=0. An isolated vertex has degree zero.

3

Count distinct neighbors from the explicit edge set to obtain deg(-5)=3. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(-4)=0. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(-3)=2. An isolated vertex has degree zero.

1

Count distinct neighbors from the explicit edge set to obtain deg(-4)=1. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(-1)=2. An isolated vertex has degree zero.

1

Count distinct neighbors from the explicit edge set to obtain deg(-1)=1. An isolated vertex has degree zero.

5

Count distinct neighbors from the explicit edge set to obtain deg(-1)=5. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(1)=0. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(3)=2. An isolated vertex has degree zero.

3

Count distinct neighbors from the explicit edge set to obtain deg(2)=3. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(7)=0. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(6)=0. An isolated vertex has degree zero.

3

Count distinct neighbors from the explicit edge set to obtain deg(7)=3. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(10)=0. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(9)=2. An isolated vertex has degree zero.

1

Count distinct neighbors from the explicit edge set to obtain deg(8)=1. An isolated vertex has degree zero.

2

Count distinct neighbors from the explicit edge set to obtain deg(11)=2. An isolated vertex has degree zero.

1

Count distinct neighbors from the explicit edge set to obtain deg(13)=1. An isolated vertex has degree zero.

5

Count distinct neighbors from the explicit edge set to obtain deg(11)=5. An isolated vertex has degree zero.

0

Count distinct neighbors from the explicit edge set to obtain deg(13)=0. An isolated vertex has degree zero.

0

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=0. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

2

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=2. Isolated vertices contribute zero, and the empty graph also gives zero.

12

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=12. Isolated vertices contribute zero, and the empty graph also gives zero.

0

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=0. Isolated vertices contribute zero, and the empty graph also gives zero.

10

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=10. Isolated vertices contribute zero, and the empty graph also gives zero.

2

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=2. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

4

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=4. Isolated vertices contribute zero, and the empty graph also gives zero.

30

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=30. Isolated vertices contribute zero, and the empty graph also gives zero.

0

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=0. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

2

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=2. Isolated vertices contribute zero, and the empty graph also gives zero.

12

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=12. Isolated vertices contribute zero, and the empty graph also gives zero.

0

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=0. Isolated vertices contribute zero, and the empty graph also gives zero.

10

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=10. Isolated vertices contribute zero, and the empty graph also gives zero.

2

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=2. Isolated vertices contribute zero, and the empty graph also gives zero.

6

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=6. Isolated vertices contribute zero, and the empty graph also gives zero.

4

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=4. Isolated vertices contribute zero, and the empty graph also gives zero.

30

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=30. Isolated vertices contribute zero, and the empty graph also gives zero.

0

Every unordered edge contributes once at each of its two endpoints, so the degree sum is 2|E|=0. Isolated vertices contribute zero, and the empty graph also gives zero.