Answered: Consider a simple graph G with 7…

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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Related questions

Question

Consider a simple graph G with 7 vertices labeled A through G. Suppose that every vertex is connected to every other vertex, except for vertex C, which is only connected to vertex A and vertex B. How many edges does the graph G have?

Expert Solution

Step 1: degrees of each vertex

$N o t e space t h a t space space space A space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x. space S o space d e g left parenthesis A right parenthesis equals 6 N o t e space t h a t space space space B space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x. space S o space d e g left parenthesis B right parenthesis equals 6 N o t e space t h a t space space space C space i s space c o n n e c t e d space t o space space A space a n d space B. space S o space d e g left parenthesis C right parenthesis equals 2 N o t e space t h a t space space space D space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x space o t h e r space t h a n space C. space S o space d e g left parenthesis D right parenthesis equals 5 N o t e space t h a t space space space E space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x space o t h e r space t h a n space C. space S o space d e g left parenthesis E right parenthesis equals 5 N o t e space t h a t space space space F space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x space o t h e r space t h a n space C. space S o space d e g left parenthesis F right parenthesis equals 5 N o t e space t h a t space space space G space i s space c o n n e c t e d space t o space e v e r y space o t h e r space v e r t e x space o t h e r space t h a n space C. space S o space d e g left parenthesis G right parenthesis equals 5$