Graph Theory

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What is Graph Theory?

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Graph Theory is a branch of mathematics that studies the properties and applications of graphs, which are structures made up of vertices (or nodes) connected by edges.

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What is a vertex in a graph?

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A vertex (or node) is a fundamental part of a graph, representing an entity or a point in the graph.

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What is an edge in a graph?

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An edge is a connection between two vertices in a graph, representing a relationship or link between them.

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What is a simple graph?

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A simple graph is a type of graph that does not contain loops or multiple edges between the same pair of vertices.

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What is a complete graph?

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A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge.

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What is a weighted graph?

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A weighted graph is a graph in which each edge has a numerical value (weight) associated with it, representing costs, distances, or other metrics.

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What is a planar graph?

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A planar graph is a graph that can be drawn on a plane without any edges crossing each other.

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What is the time complexity of Depth-First Search (DFS)?

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O(V + E), where V is the number of vertices and E is the number of edges.

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What is the time complexity of Breadth-First Search (BFS) using an adjacency list?

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O(E + V), where E is the number of edges and V is the number of vertices.

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What is Kruskal’s algorithm used for?

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Kruskal’s algorithm is used to find the Minimum Spanning Tree (MST) of a graph.