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No its not. A cycle is closed trail

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Q: Is cycle and circuit in graph theory same?
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What is a cycle in graph theory?

If the graph start and end with same vertex and no other vertex can be repeated then it is called trivial graph.


Find any Hamiltonian circuit on the graph above. Give your answer as a list of vertices, starting and ending at the same vertex. Example: ABCA?

connecting the vertices in a graph so that the route traveled starts and ends at the same vertex.


Prove that if a DFS and BFS trees in graph G are the same than?

ok here we go...Proof:If the some graph G has the same DFS and BFS then that means that G should not have any cycle(work out for any G with a cycle u will never get the same BFS and DFS .... and for a graph without any cycle u will get the same BFS/DFS).We will prove it by contradiction:So say if T is the tree obtained by BFS/DFS, and let us assume that G has atleast one edge more than T. So one more edge to T(T is a tree) would result in a cycle in G, but according to the above established principle no graph which has a cycle would result the same DFS and BFS, so out assumption is a contradiction.Hence G should have more edges than T, which implies that if the BFS and DFS for a graph G are the same then the G = T.Hope this helps u......................


How can the reduction from independent set to vertex cover be used to determine the relationship between the two concepts in graph theory?

The reduction from independent set to vertex cover in graph theory helps show that finding a vertex cover in a graph is closely related to finding an independent set in the same graph. This means that solving one problem can help us understand and potentially solve the other problem more efficiently.


Can you plot the same things from a frequency graph on a line graph?

yes you can plot same things from a frequency graph on a line graph because it is the same thing :) peace


What is the cycle property of minimum spanning trees (MSTs) and how does it impact the construction and optimization of MSTs?

The cycle property of minimum spanning trees (MSTs) states that if you have a cycle in a graph and you remove the heaviest edge from that cycle, the resulting graph will still have the same minimum spanning tree. This property impacts the construction and optimization of MSTs by helping to identify and eliminate unnecessary edges, leading to a more efficient and optimal tree structure.


What is the significance of the 2 coloring problem in graph theory and how does it relate to other concepts in the field?

The significance of the 2-coloring problem in graph theory lies in its simplicity and fundamental nature. It involves coloring the vertices of a graph with only two colors such that no adjacent vertices have the same color. This problem is important because it helps in understanding the concept of graph coloring and can be used as a building block for more complex problems in graph theory, such as the chromatic number and the four-color theorem. The 2-coloring problem also has applications in various real-world scenarios, such as scheduling and map coloring.


Is a circle graph the same as a pie graph?

yes


What is a double line graph?

a double line graph is a graph that is same as a line graph but there are two lines


Where does the negative sign go in imaginary numbers?

The basic theory of imaginary numbers is that because (-) numbers squared are the same as (+) numbers squared there is not a correct continueos line on a graph.


Is broken line graph same as the line graph?

no because the broken line graph is a line graph that is broken da!


Is the current the same everywhere in the parallel circuit?

No. The current in a series circuit is the same everywhere. The voltage across a parallel circuit is the same.