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Ksi7 is not Show that ksit regular. is not

Ksi7 is not Show that ksit regular. is not

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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### Problem 14 Show that \( K_{5,7} \) is not regular. ### Explanation In graph theory, a regular graph is one where each vertex has the same degree. \( K_{5,7} \) is a complete bipartite graph which means it is divided into two disjoint vertex sets, with 5 vertices in one set and 7 in the other. Every vertex from one set is connected to every vertex in the other set. To determine if \( K_{5,7} \) is regular, we need to check if all vertices have the same degree. In \( K_{5,7} \): - Each of the 5 vertices in the first set is connected to all 7 vertices in the second set, so each has a degree of 7. - Each of the 7 vertices in the second set is connected to all 5 vertices in the first set, so each has a degree of 5. Since the degrees are different (7 and 5), \( K_{5,7} \) is not a regular graph.
Transcribed Image Text:### Problem 14 Show that \( K_{5,7} \) is not regular. ### Explanation In graph theory, a regular graph is one where each vertex has the same degree. \( K_{5,7} \) is a complete bipartite graph which means it is divided into two disjoint vertex sets, with 5 vertices in one set and 7 in the other. Every vertex from one set is connected to every vertex in the other set. To determine if \( K_{5,7} \) is regular, we need to check if all vertices have the same degree. In \( K_{5,7} \): - Each of the 5 vertices in the first set is connected to all 7 vertices in the second set, so each has a degree of 7. - Each of the 7 vertices in the second set is connected to all 5 vertices in the first set, so each has a degree of 5. Since the degrees are different (7 and 5), \( K_{5,7} \) is not a regular graph.
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