Are the following statements true or false? T or F A) Any graph with an Euler trail that is not an Euler circuit can be made into a graph with an Euler circuit by adding a single edge.  T or F B) If a graph has an Euler trail but not an Euler circuit, then every Euler trail must start at a vertex of odd degree.  T or F C) If a complte graph has an Euler circuit, then the graph has an odd number of vertices.  T or F D) Every graph in which every vertex has even degree has an Euler circuit.  T or F E) Every graph with an Euler trail is connected.

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A:

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Q: Give two properties of a graph that nsures that it possesses an Euler Circuit

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Graph theory

It is that part of network analysis where the configuration is called graph or structure of the network system when all of the elements (e.g., R, L, and C) in a network system are substituted with lines having circles/rings or dots across both endpoints. The study of the solution of the networks and circuits with the help of graphs is known as graph theory. The objective is to know the mathematics behind the network analysis.