EXCURSIONS IN MATHMATICS

If there is at least one edge connecting two vertices in a​ graph, the vertices are called​ _____.

Adjacent

If an edge is removed from a connected graph and leaves behind a disconnected​ graph, such an edge is called a​ _____.

Bridge

When using this algorithm and faced with a choice of edges to​ trace, choose an edge that is not​ a/an _______.

Bridge

If this sequence of vertices and connecting edges begins and ends at the same​ vertex, it is called a​ _____.

Circuit

The number of edges that connect to a vertex is called the​ _____ of the vertex

Degree

A connected graph has even vertices​ A, B, and​ C, and odd​ vertices, D and E. Each Euler path must begin at vertex D and end at vertex​ _______, or begin at vertex​ _______ and end at vertex​ _______.

E E D

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.

Fleury's Bridge

A sequence of such vertices and the edges connecting them is called a​ _____.

Path

Every Euler path is an Euler circuit. True or false.

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.