1,911 views
4 votes
4 votes

Which of the following Graph has Euler Path but is not an Euler Graph?
A. K1,1 
B.K2,10 
C.K2,11
D.K10,11.

2 Answers

1 votes
1 votes
option A is right

euler path is possible but euler cycle is not possible so it is not a euler graph
0 votes
0 votes

The degree-sequence of a Complete Bipartite Graph $K_{p,q}$ is  $(p,p,...,p,q,...,q)$  where p is repeated q times and q is repeated p times. Therefore, $K_{2,11}$ would have a degree sequence (2,2,2,2,2,2,2,2,2,2,2,11,11). 

Since $K_{2,11}$ is a connected graph with exactly two of its vertices having odd degrees while remaining having even degrees, it will have a Euler path.

Hence options A and C would be right.

Also read,

https://math.stackexchange.com/questions/221512/hamilton-euler-circuit-path

edited by

Related questions

0 votes
0 votes
3 answers
1
Bongbirdie asked Apr 1, 2017
624 views
What is the difference between path and Euler path?