0 0 votes Is it possible that a disconnected graph be an Euler graph ? Graph Theory graph-theory euler-graph + – jatin khachane 1 3.6k views answer comment Share Follow Print See all 11 Comments 11 11 Comments reply Hemanth_13 commented Dec 24, 2018 reply Follow flag I think no as you need a cycle with every edge atleast once 0 0 replyShare jatin khachane 1 commented Dec 24, 2018 reply Follow flag https://math.stackexchange.com/questions/1414667/is-it-possible-disconnected-graph-has-euler-circuit 1 1 replyShare smsubham commented Dec 24, 2018 reply Follow flag Yes possible. An example is graph having C3 + isolated vertex, 0 0 replyShare jatin khachane 1 commented Dec 24, 2018 reply Follow flag check this here also degree of each vertex is even but not euler 0 0 replyShare Shaik Masthan commented Dec 24, 2018 reply Follow flag if disconnected graph has to be Euler graph, that is disconnect due to isolated vertices only 2 2 replyShare jatin khachane 1 commented Dec 24, 2018 reply Follow flag I think disconnected graph should not be euler ..as there will not be a path such that every edge is visited exactly once 0 0 replyShare prashant jha 1 commented Jan 1, 2019 reply Follow flag Euler graph always has to be connected. 0 0 replyShare Magma commented Jan 1, 2019 reply Follow flag never 0 0 replyShare Gupta731 commented Jan 1, 2019 reply Follow flag Euler graph is always connected 0 0 replyShare Shaik Masthan commented Jan 1, 2019 reply Follow flag if that graph is disconnected due to isolated vertex, then yes that graph is euler ! 0 0 replyShare avadh commented Jan 10, 2019 reply Follow flag false 0 0 replyShare Please log in or register to add a comment.
1 1 vote disconnected graph can have an Euler circuit. That's because an Euler circuit is only required to traverse every edge of the graph, it's not required to visit every vertex; so isolated vertices are not a problem. A graph is connected enough for an Euler circuit if all the edges belong to one and the same component manisha11 answered Sep 17, 2020 manisha11 comment Share Follow 0 reply Please log in or register to add a comment.
0 0 votes No, as the basic definition of Euler graph is standardized to only Connected Graphs. anbor777 answered Sep 22, 2020 anbor777 comment Share Follow 0 reply Please log in or register to add a comment.
–1 –1 vote not possible to form a closed trail by a disconnected graph hence not euler TUSHAR_BHATT answered Dec 24, 2018 TUSHAR_BHATT comment Share Follow 0 reply Please log in or register to add a comment.
