5. Find the number of connected components in the following graphs. (a) V(G) = Z. Edges: m and n are adjacent if and only if |m- n = 5. (b) V(G) = Z. Edges: m and n are adjacent if and only if |m-n| = 15 or |m-n| = 6. (c) V(G) = Zx Z. Edges: (a, b) is adjacent to (c,d) if and only if (la - c = 4 and |bd|= 0) or (ac|= 0 and |bd| = 7). (d) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) =(4,2) or (c-a, d-b) = (-4,-2) or (c-a, d-b) = (1, 2) or (c-a, d-b) = (-1,-2). (e) V(G) = ZxZ. Edges: (a, b) is adjacent to (c,d) if and only if (c-a, d-b)=(5,2) or (c-a, d-b) = (-5,-2) or (c-a, d-b) = (2,3) or (c-a, d-b) = (-2,-3). (f) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (7,2) or (c-a, d-b) = (-7,-2) or (c-a, d-b) = (3, 1) or (c-a, d-b) = (-3,-1).
5. Find the number of connected components in the following graphs. (a) V(G) = Z. Edges: m and n are adjacent if and only if |m- n = 5. (b) V(G) = Z. Edges: m and n are adjacent if and only if |m-n| = 15 or |m-n| = 6. (c) V(G) = Zx Z. Edges: (a, b) is adjacent to (c,d) if and only if (la - c = 4 and |bd|= 0) or (ac|= 0 and |bd| = 7). (d) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) =(4,2) or (c-a, d-b) = (-4,-2) or (c-a, d-b) = (1, 2) or (c-a, d-b) = (-1,-2). (e) V(G) = ZxZ. Edges: (a, b) is adjacent to (c,d) if and only if (c-a, d-b)=(5,2) or (c-a, d-b) = (-5,-2) or (c-a, d-b) = (2,3) or (c-a, d-b) = (-2,-3). (f) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (7,2) or (c-a, d-b) = (-7,-2) or (c-a, d-b) = (3, 1) or (c-a, d-b) = (-3,-1).
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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![5. Find the number of connected components in the following graphs.
(a) V(G) = Z. Edges: m and n are adjacent if and only if |mn| = 5.
(b) V(G) = Z. Edges: m and n are adjacent if and only if |m-n| = 15 or |m-n| = 6.
(c) V(G) = Zx Z. Edges: (a, b) is adjacent to (c,d) if and only if (la - c = 4 and
|bd|= 0) or (la c = 0 and b-d] =7).
(d) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (4,2)
or (ca, db) = (-4,-2) or (c-a, d-b) = (1, 2) or (c-a, d-b) = (-1,-2).
(e) V(G) = ZxZ. Edges: (a, b) is adjacent to (c,d) if and only if (c-a, d-b) = (5,2)
or (c-a, d-b) = (-5, -2) or (c-a, d-b) = (2,3) or (c-a, d-b) = (-2,-3).
(f) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (7,2)
or (c-a, d-b) = (-7,-2) or (c-a, d-b) = (3, 1) or (c-a, d-b) = (-3,-1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd580b721-3664-446f-9ceb-e2cc456c38cd%2F26896376-93c5-437b-a32c-159d7ecf2142%2Fr9zxrimn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Find the number of connected components in the following graphs.
(a) V(G) = Z. Edges: m and n are adjacent if and only if |mn| = 5.
(b) V(G) = Z. Edges: m and n are adjacent if and only if |m-n| = 15 or |m-n| = 6.
(c) V(G) = Zx Z. Edges: (a, b) is adjacent to (c,d) if and only if (la - c = 4 and
|bd|= 0) or (la c = 0 and b-d] =7).
(d) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (4,2)
or (ca, db) = (-4,-2) or (c-a, d-b) = (1, 2) or (c-a, d-b) = (-1,-2).
(e) V(G) = ZxZ. Edges: (a, b) is adjacent to (c,d) if and only if (c-a, d-b) = (5,2)
or (c-a, d-b) = (-5, -2) or (c-a, d-b) = (2,3) or (c-a, d-b) = (-2,-3).
(f) V(G) = ZxZ. Edges: (a, b) is adjacent to (c, d) if and only if (c-a, d-b) = (7,2)
or (c-a, d-b) = (-7,-2) or (c-a, d-b) = (3, 1) or (c-a, d-b) = (-3,-1).
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