Use the formula deg(v) = 2|E(G)| to find the number of edges of the following VEV (G) graphs. Classify (count) the vertices by number of neighbors. (a) V(G) = [100]. Edges: for all n and m in [100], n ‡ m, n is adjacent to m if and only if |nm| ≤ 4. (b) V(G) × = = [10] [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) (c,d), (a, b) is adjacent to (c,d) if and only if a = c or b= d. = (c) V(G) [10] x [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d), (a, b) is adjacent to (c,d) if and only if |ac| + |bd| = 1. (c,d), (d) V(G) [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × = (a, b) is adjacent to (c,d) if and only if |ac| + |bd| ≤ 2. - [10], (a, b)
Use the formula deg(v) = 2|E(G)| to find the number of edges of the following VEV (G) graphs. Classify (count) the vertices by number of neighbors. (a) V(G) = [100]. Edges: for all n and m in [100], n ‡ m, n is adjacent to m if and only if |nm| ≤ 4. (b) V(G) × = = [10] [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) (c,d), (a, b) is adjacent to (c,d) if and only if a = c or b= d. = (c) V(G) [10] x [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d), (a, b) is adjacent to (c,d) if and only if |ac| + |bd| = 1. (c,d), (d) V(G) [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × = (a, b) is adjacent to (c,d) if and only if |ac| + |bd| ≤ 2. - [10], (a, b)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Use the formula
deg(v) = 2|E(G)| to find the number of edges of the following
vЄV (G)
graphs. Classify (count) the vertices by number of neighbors.
(a) V(G) = [100]. Edges: for all n and m in [100], n ‡ m, n is adjacent to m if and
only if |nm| ≤ 4.
(b) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d),
(a, b) is adjacent to (c,d) if and only if a = c or b = d.
(c) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d),
(a, b) is adjacent to (c,d) if and only if |ac| + |bd| = 1.
(d) V (G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10],
(a, b) is adjacent to (c,d) if and only if |a - c + b-d ≤ 2.
(a, b) ‡ (c,d),](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc06da2-7bd8-42a3-b8a1-3f8b831a8034%2Fccefdfa5-22d7-4199-946c-52472d683137%2F2hcs25v_processed.png&w=3840&q=75)
Transcribed Image Text:Use the formula
deg(v) = 2|E(G)| to find the number of edges of the following
vЄV (G)
graphs. Classify (count) the vertices by number of neighbors.
(a) V(G) = [100]. Edges: for all n and m in [100], n ‡ m, n is adjacent to m if and
only if |nm| ≤ 4.
(b) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d),
(a, b) is adjacent to (c,d) if and only if a = c or b = d.
(c) V(G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10], (a, b) ‡ (c,d),
(a, b) is adjacent to (c,d) if and only if |ac| + |bd| = 1.
(d) V (G) = [10] × [10]. Edges: for all (a, b) and (c,d) in [10] × [10],
(a, b) is adjacent to (c,d) if and only if |a - c + b-d ≤ 2.
(a, b) ‡ (c,d),
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