# Graph Theory Discrete Mathematics Study Notes (Part-1)

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Graph Theory Discrete Mathematics Study Notes (Part-1)- Graph: A graph G is defined by G = (V, E) where V is the set of all vertices in G and E is the set of all edges in G. Graph Theory comes under discrete mathematics which is conducted in 2 part first contains Graph, Theorems, Trees and types, Regular Graph, Edge Connectivity.

This topic is important for various competitive exams such as GATE CE, SSC JE, ISRO, ESE, IES and other computer science exams.

Table of content

## Graph Notes

• Isolated Vertex: A vertex with degree zero is called an isolated vertex or lone vertex.
• Null Graph: A graph with no edges is called a null graph.
• Simple Graph: A graph with no parallel edges and no loops is called a simple graph.
• Directed Graph: In a digraph, an edge (u, v) is said to be from u to v.
• Undirected Graph: In an undirected graph an edge {u, v} is said to join u and v or to be between u and v.
• Pendant Vertex: A vertex with degree one is called a Pendant vertex.
• Path: It is the sequence of edges, without vertex repetition.
• Network: It is a graph with only one source and one sink.
• Trial (Tour or Walk): It is the sequence of edges without edge repetition (vertex may repeat).
• Independence Number: Number of vertices in a largest maximal independent set.
• The diameter of a Graph: Maximum distance between any two vertices in a graph.
• Loop: An edge is drawn from a vertex to itself.
• Trivial Graph: A graph with no edges and one vertex.
• Discrete Graph or Null Graph: A graph with only isolated vertices and no edges.
• Pseudo Graph: A graph in which self-loops are allowed as well as parallel or multiple edges are allowed.

## Edge Connectivity

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