Graph Theory Calculator

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Example

Created on 2024-06-20Asked by Luna Scott (Solvelet student)

Determine if the given graph is bipartite:

G = (V, E)

where

V = \{1, 2, 3, 4\}

and

E = \{(1, 2), (2, 3), (3, 4), (4, 1)\}

Solution

To determine if the given graph is bipartite: 1. Attempt to color the graph using two colors such that no two adjacent vertices share the same color. Graph

G

: - Vertices:

V = \{1, 2, 3, 4\}

- Edges:

E = \{(1, 2), (2, 3), (3, 4), (4, 1)\}

Color vertex 1 with color A. Color vertex 2 with color B (since it's adjacent to 1). Color vertex 3 with color A (since it's adjacent to 2). Color vertex 4 with color B (since it's adjacent to 3). The graph can be colored with two colors without two adjacent vertices sharing the same color: - Vertex 1: A - Vertex 2: B - Vertex 3: A - Vertex 4: B Therefore, the graph is bipartite. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Abigail Martin on Solvelet

1. Determine whether the graph

G = (V, E)

with

V = \{1, 2, 3, 4\}

and

E = \{\{1, 2\}, \{2, 3\}, \{3, 4\}, \{4, 1\}\}

is connected,2. Find the shortest path between vertices

A

and

B

in the graph

G = (V, E)

with

V = \{A, B, C, D\}

and

E = \{\{A, B\}, \{B, C\}, \{C, D\}, \{D, A\}\}

DefinitionA graph is essentially a collection of nodes and links and graph theory is the branch of mathematics that studies these in detail. Directed versus undirected and weighted versus unweighted graphs are also considered, and in general, they are used to encode the relationships and interactions within a variety of systems. Graph theory is a rich field of mathematics with applications to networking, routing, logic puzzles, and more. They manifest in many domains, from computer science (networking, algorithms), biology (gene networks), social sciences (social networks) to engineering (circuit design). Example: A graph G=(V,E) where V corresponds to the set of vertices and E corresponds to the set of edges that connect pairs of vertices.

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