What are the two main components of a graph?

Vertices and edges

The degree of a graph is defined as the number of ______ incident on a node.

Edges

True or False: A cycle in a graph is defined as a path that visits all edges and nodes at least once.

False. A cycle is a closed path in which all the edges are different.

In a directed graph, what does it mean if a branch is oriented towards a node?

It means the branch enters the node.

Riddle: I connect vertices and can be directed or undirected, but I am not a point. What am I?

Edge

Fill in the blank: A tree is an interconnected open set of branches which include all the nodes of the given graph, and it cannot have any ______.

Closed loops

What is the relationship between the number of twigs (T) and the number of nodes (N) in a tree?

T = N - 1

Which matrix shows which branch is incident to which node?

Incidence Matrix

True or False: A connected graph has at least one path along branches between every pair of vertices.

True

In a fundamental cut set, how many twigs are typically involved?

One twig

What is the size of the incidence matrix if a graph contains N nodes and B branches?

N x B

Riddle: I can form loops when added to a tree but am not part of it. What am I?

Link or chord

Fill in the blank: The elements of the fundamental cut-set matrix are defined as +1 if the jth branch is incident to the ith cut set and oriented in the ______ direction.

Same

What is a subgraph?

A graph that consists of some nodes and edges from a larger graph.

Which type of graph is characterized by having edges that do not overlap?

Planar graph