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For m, n > 1, define the grid graph Gm.n to have vertex set V = {(i, j) | 1< i

For m, n > 1, define the grid graph Gm.n to have vertex set V = {(i, j) | 1< i

Advanced Engineering Mathematics
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. For m, n > 1, define the grid graph Gm.n to have vertex set V = {(i, j) | 1 <i<m, 1<j< n}, and edge set E given by: one edge from (i, j) to (i+1, j) for 1<i<m (and every j), and one edge from (i, j) to (i, j+ 1) for 1 <j<n (and every i). For example, the grid graph G3,2 is: (1,1) (2,1) (3,1) (1,2) (2,2) (3,2) Find a maximal matching and a minimal vertex cover for the grid graph Gmn, and thereby determine m(Gm,n) and vc(Gm,n).
Transcribed Image Text:5. For m, n > 1, define the grid graph Gm.n to have vertex set V = {(i, j) | 1 <i<m, 1<j< n}, and edge set E given by: one edge from (i, j) to (i+1, j) for 1<i<m (and every j), and one edge from (i, j) to (i, j+ 1) for 1 <j<n (and every i). For example, the grid graph G3,2 is: (1,1) (2,1) (3,1) (1,2) (2,2) (3,2) Find a maximal matching and a minimal vertex cover for the grid graph Gmn, and thereby determine m(Gm,n) and vc(Gm,n).
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