SHAURYA KHURANA
@jamwine
Public Graphs
Icosahedron Graph (5-Regular)
The graph of an icosahedron is 5-regular with 12 vertices and 30 edges. Each ve…
Octahedron Graph (4-Regular)
The graph of an octahedron is 4-regular with 6 vertices and 12 edges. Each vert…
Cube Graph (3-Regular)
The graph of a cube is 3-regular with 8 vertices and 12 edges. Each vertex has …
Cycle C₄ (Square)
A square is a 2-regular graph of order 4. Every vertex in a cycle has exactly 2…
Solution: K6 Complete Graph (5-Regular)
Complete graph K6 where each of 6 vertices connects to all other 5 vertices. Th…
Solution: 4-Regular of Order 6
A hexagon with additional edges. Each vertex has degree 4.
Solution: K5 Complete Graph (4-Regular)
Complete graph K5 where each of 5 vertices connects to all other 4 vertices. Th…
Solution: 2-Regular of Order 3 (Triangle)
A triangle (cycle C3). Each vertex has degree 2, forming a 3-cycle.
Solution: 1-Regular of Order 6
Three disconnected edges forming a perfect matching with 6 vertices.
Solution: 1-Regular of Order 2
A single edge connecting two vertices. Each vertex has degree 1.
Complete Graph K4 (3-Regular)
The complete graph K4 is 3-regular. Each of the 4 vertices connects to all 3 ot…
2-Regular Graph (Order 5)
A 2-regular graph forming a pentagon (cycle C5). Each vertex has degree 2, crea…
1-Regular Graph (Order 4)
A 1-regular graph with 4 vertices forming two disconnected edges (perfect match…
3-Regular Graph (Order 6)
A 3-regular graph with 6 vertices. Every vertex has degree 3. This graph is for…
Pigeonhole Coloring Example
A graph with 12 vertices demonstrating that with only 10 colors, some colors mu…
Havel-Hakimi Example Graph
A graph with degree sequence [3, 3, 2, 2, 2] demonstrating the Havel-Hakimi alg…
Road Network Example
A simple road network connecting four towns: Springfield, Riverside, Hilltop, a…
Handshaking Lemma Demonstration
Graph with 5 edges showing sum of degrees = 2 × 5 = 10
Minimum and Maximum Degree
Graph showing δ(G)=1 (minimum degree) and Δ(G)=4 (maximum degree)
Regular Graph - All Same Degree
A 2-regular graph where every vertex has degree 2
Non-Graphic Sequence Demo
Attempting sequence (4,3,2,1) - impossible configuration
Degree Sequence Example
Graph with degree sequence (3, 3, 2, 1, 1, 0)
Graph with Isolated Vertex
Graph showing an isolated vertex (degree 0) and various other degrees
Complete Graph K4 - Maximum Size
Complete graph with 4 vertices showing maximum possible edges: 4(4-1)/2 = 6 edg…
Small Graph - Order 4
A simple graph with 4 vertices and 3 edges to demonstrate order and size
Simple Tree
A tree structure with no cycles, showing a hierarchical relationship.
Bipartite Job Applicants
A bipartite graph showing job applicants and the positions they qualify for.
Flight Map
A map connecting a few major cities
One-Way Streets
A directed graph showing one-way streets between intersections A, B, and C.
Undirected Friendship Graph
An example showing symmetric friendships in an undirected graph.
Simple Social Network
A basic example of a social network showing friendships between Alice, Bob, Cha…
Graph Representation
Several ways of drawing the same graph
Graph Examples
Graphs are networks of points and lines