Star Graphs S1-S5
A colored graph containing star graphs S1 through S5
Last modified: Jun 11, 2026
Complete Graph K4 - Maximum Size
Complete graph with 4 vertices showing maximum possible edges: 4(4-1)/2 = 6 edges
Last modified: Dec 27, 2025
Graph with Isolated Vertex
Graph showing an isolated vertex (degree 0) and various other degrees
Last modified: Dec 27, 2025
Degree Sequence Example
Graph with degree sequence (3, 3, 2, 1, 1, 0)
Last modified: Dec 27, 2025
Non-Graphic Sequence Demo
Attempting sequence (4,3,2,1) - impossible configuration
Last modified: Dec 27, 2025
Regular Graph - All Same Degree
A 2-regular graph where every vertex has degree 2
Last modified: Dec 27, 2025
Minimum and Maximum Degree
Graph showing δ(G)=1 (minimum degree) and Δ(G)=4 (maximum degree)
Last modified: Dec 27, 2025
Handshaking Lemma Demonstration
Graph with 5 edges showing sum of degrees = 2 × 5 = 10
Last modified: Dec 27, 2025
Road Network Example
A simple road network connecting four towns: Springfield, Riverside, Hilltop, and Lakeside. This gr…
Last modified: Dec 27, 2025
Havel-Hakimi Example Graph
A graph with degree sequence [3, 3, 2, 2, 2] demonstrating the Havel-Hakimi algorithm. Vertex A and…
Last modified: Dec 27, 2025
Small Graph - Order 4
A simple graph with 4 vertices and 3 edges to demonstrate order and size
Last modified: Dec 27, 2025
Pigeonhole Coloring Example
A graph with 12 vertices demonstrating that with only 10 colors, some colors must repeat. Notice ve…
Last modified: Dec 27, 2025
3-Regular Graph (Order 6)
A 3-regular graph with 6 vertices. Every vertex has degree 3. This graph is formed by a hexagon wit…
Last modified: Dec 27, 2025
1-Regular Graph (Order 4)
A 1-regular graph with 4 vertices forming two disconnected edges (perfect matching). Each vertex ha…
Last modified: Dec 27, 2025
2-Regular Graph (Order 5)
A 2-regular graph forming a pentagon (cycle C5). Each vertex has degree 2, creating a single cycle.
Last modified: Dec 27, 2025
Complete Graph K4 (3-Regular)
The complete graph K4 is 3-regular. Each of the 4 vertices connects to all 3 other vertices.
Last modified: Dec 27, 2025
Solution: 1-Regular of Order 2
A single edge connecting two vertices. Each vertex has degree 1.
Last modified: Dec 27, 2025
Solution: 1-Regular of Order 6
Three disconnected edges forming a perfect matching with 6 vertices.
Last modified: Dec 27, 2025
Solution: 2-Regular of Order 3 (Triangle)
A triangle (cycle C3). Each vertex has degree 2, forming a 3-cycle.
Last modified: Dec 27, 2025
Solution: K5 Complete Graph (4-Regular)
Complete graph K5 where each of 5 vertices connects to all other 4 vertices. This is 4-regular.
Last modified: Dec 27, 2025
Solution: 4-Regular of Order 6
A hexagon with additional edges. Each vertex has degree 4.
Last modified: Dec 27, 2025
Solution: K6 Complete Graph (5-Regular)
Complete graph K6 where each of 6 vertices connects to all other 5 vertices. This is 5-regular.
Last modified: Dec 27, 2025
Cube Graph (3-Regular)
The graph of a cube is 3-regular with 8 vertices and 12 edges. Each vertex has degree 3.
Last modified: Dec 27, 2025
Octahedron Graph (4-Regular)
The graph of an octahedron is 4-regular with 6 vertices and 12 edges. Each vertex connects to 4 oth…
Last modified: Dec 27, 2025
Cycle C₄ (Square)
A square is a 2-regular graph of order 4. Every vertex in a cycle has exactly 2 neighbors.
Last modified: Dec 27, 2025
Icosahedron Graph (5-Regular)
The graph of an icosahedron is 5-regular with 12 vertices and 30 edges. Each vertex connects to 5 o…
Last modified: Dec 27, 2025
Simple Tree
A tree structure with no cycles, showing a hierarchical relationship.
Last modified: Nov 04, 2025
Flight Map
A map connecting a few major cities
Last modified: Nov 04, 2025
Bipartite Job Applicants
A bipartite graph showing job applicants and the positions they qualify for.
Last modified: Nov 04, 2025
One-Way Streets
A directed graph showing one-way streets between intersections A, B, and C.
Last modified: Nov 04, 2025
Undirected Friendship Graph
An example showing symmetric friendships in an undirected graph.
Last modified: Nov 04, 2025
Simple Social Network
A basic example of a social network showing friendships between Alice, Bob, Charlie, and Diana.
Last modified: Nov 04, 2025
Graph Representation
Several ways of drawing the same graph
Last modified: Jul 24, 2025
Graph Examples
Graphs are networks of points and lines
Last modified: Jul 24, 2025
Petersen Graph
The Petersen graph, a well-known counterexample in graph theory
Last modified: Jul 22, 2025
Cycle Graphs C1-C6
A graph containing cycle graphs C1 through C6 as disconnected components
Last modified: Jul 22, 2025
Complete Graph K4
A complete graph with 4 vertices and 6 edges (K4)
Last modified: Jul 22, 2025
Complete Graph K5
A complete graph with 5 vertices and 10 edges (K5)
Last modified: Jul 22, 2025
Complete Graphs K1, K2, K3
A graph containing K1, K2, and K3 as disconnected components
Last modified: Jul 22, 2025