Graph Theory

Question

consider the following statement-:

1.If a graph has Euler circuit then it is Strongly Connected graph.

2.If a graph has Euler path(but not Euler circuit) then it is Strongly Connected graph.

3.If a graph has Euler circuit then it is Weakly Connected graph.

4.If a graph has Euler path(but not euler circuit) then it is Weakly Connected graph.

Which statement is true with proper explanation.

Comments

Not every Euler/Unicursal graph is connected.and not every graph with even degree is Eulerian graph.

Answer 1

1. Should be ans...

Euler path visit each edge exactly once...

And in that if starting vertex and ending vertex is same than called circuit..

Euler circuitgenerates cycle of n-1 edges ...

And it is maximal connected component..

Comments

@Gabbar If a graph is having a isolated vertex and a cycle .than it is having euler cycle but it is not strongly connected .
and i this scenario all options are wrong beacuse we can find the contradictory example for each case.

Answer 2

Answer is 1 because:

if there is an euler circuit in the graph then that means there exists a closed path that traverses all the edges of the graph exactly once. This means every vertex is reachable from every other vertex. Hence Strongly connected.

Comments

i think two option is correct option (1) and option (3)

for option 3 we know all strongly connected component is also a weakly connected component.