math

A path that passes through each edge of a graph exactly one time is called​ a(n) ______ path.

Euler

A circuit that travels through every edge of a graph exactly once is called​ a/an _______ circuit.

Euler circuit

Every Euler path is an Euler circuit.

The statement is false because both an Euler circuit and an Euler path are paths that travel through every edge of a graph once and only once. An Euler circuit also begins and ends on the same vertex. An Euler path does not have to begin and end on the same vertex.

Every Euler circuit is an Euler path.

The statement is true because both an Euler circuit and an Euler path are paths that travel through every edge of a graph once and only once. An Euler circuit also begins and ends on the same vertex.

A connected graph has at least one Euler​ circuit, which, by​ definition, is also an Euler​ path, if the graph has​ _______ odd vertices. An Euler circuit can start and end at​ _______ vertex.

no, any

A connected graph has no Euler paths and no Euler circuits if the graph has more than two​ _______ vertices

odd

A connected graph has at least one Euler​ path, but no Euler​ circuit, if the graph has exactly​ _______ odd​ vertices/vertex.

two

​Euler's Theorem enables us to count a​ graph's odd vertices and determine if it has an Euler path or an Euler circuit. A procedure for finding such paths and circuits is called​ _______ Algorithm. When using this algorithm and faced with a choice of edges to​ trace, choose an edge that is not​ a/an _______. Travel over such an edge only if there is no alternative

​Fleury's, bridge