0 votes 0 votes In a connected simple graph with 30 edges the maximum number of vertices possible are Vipin Rai asked Nov 29, 2018 Vipin Rai 1.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes As the graph is a simple connected graph , for a simple connected graph with n vertices minimum no of edges is n-1. So n-1=30 implies n=31 anjali007 answered Nov 29, 2018 • selected Nov 29, 2018 by Vipin Rai anjali007 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes A graph with n vertices has $\frac{n\left ( n-1 \right )}{2}$ edges $\therefore \frac{n(n-1)}{2} = 30$ n(n-1) = 60 n2-n=60 n2-n-60=0 Applying Sridharacharya formula, we get n = 8 (approx) Eliminating one of the roots as vertices cannot be negative. Gupta731 answered Nov 29, 2018 • edited Nov 29, 2018 by Gupta731 Gupta731 comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments Gupta731 commented Nov 29, 2018 reply Follow Share https://math.stackexchange.com/questions/1570642/graph-theory-show-maximum-number-of-edges-in-a-simple-graph 0 votes 0 votes anjali007 commented Nov 29, 2018 reply Follow Share @Vipin Rai yup vertices =31 0 votes 0 votes anjali007 commented Nov 29, 2018 reply Follow Share @Gupta731 it is the case for minimum number of vertices and maximum number of edges 0 votes 0 votes Please log in or register to add a comment.