0 votes 0 votes $G$ be a simple graph on $8$ vertices such that there is a vertices of degrees $1,2,3,4,5,6,7$ respectively, Then which of the following can be the degree of the last vertex$?$ $3$ $0$ $5$ $4$ Graph Theory discrete-mathematics graph-theory degree-of-vertices virtual-gate-test-series + – smartmeet asked Jan 27, 2017 edited Apr 4, 2019 by Lakshman Bhaiya smartmeet 507 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes The vertex should be even as there are already even number of odd vertices so A and C are eliminated ...Either I can go with 0 or 4 ...0 is not possible as it wil not give simple graph by Havel hakimi theorem but 4 can give simple graph so answer is D Pavan Kumar Munnam answered Jan 27, 2017 selected Jan 28, 2017 by Sushant Gokhale Pavan Kumar Munnam comment Share Follow See all 0 reply Please log in or register to add a comment.