All Math Department Calculator Related Post

    Dominating Set Finder Enter Undirected Edges (u v) one per line: Search Method: Exact (Brute-Force, n≤20)Greedy Approximation Find Dominating Set * Based on Haynes et al. (1998) definitions and greedy ln(Δ+1) approximation. A set S dominates if every vertex not in S is adjacent to S. About the Dominating Set Finder The Dominating […]

    Vertex Coloring Calculator Enter Undirected Edges (u v) one per line: Color Vertices * Based on greedy coloring and Brooks’ theorem: χ(G) ≤ Δ+1. Uses optimal Δ+1 bound. Planar graphs need ≤4 colors (Four Color Theorem). About the Vertex Coloring Calculator The Vertex Coloring Calculator is a fundamental graph theory tool that computes

    Edge Coloring Calculator Enter Undirected Edges (u v) one per line: Color Edges * Based on Vizing’s theorem: χ'(G) = Δ or Δ+1. Uses greedy coloring with optimal Δ+1 bound. Bipartite graphs are class 1 (χ’ = Δ). About the Edge Coloring Calculator The Edge Coloring Calculator is a combinatorial optimization tool that

    Articulation Point Finder Enter Undirected Edges (u v) one per line: Find Articulation Points * Based on Tarjan’s DFS with discovery time and low values. An articulation point (cut vertex) increases the number of connected components when removed. About the Articulation Point Finder The Articulation Point Finder is a graph robustness analysis tool

    Bridge and Cut Vertex Finder Enter Undirected Edges (u v) one per line: Find Bridges & Cut Vertices * Based on Tarjan’s DFS with discovery time and low values. A bridge is an edge whose removal increases components. A cut vertex increases components when removed. About the Bridge and Cut Vertex Finder The

    Incidence Graph Generator Enter Blocks (one per line, elements space-separated): Layout Style: Force-DirectedBipartite (Top/Bottom) Generate Incidence Graph * Based on Levi graph construction: vertices for points and lines, edges for incidence. Also known as the incidence graph of a set system. About the Incidence Graph Generator The Incidence Graph Generator is a combinatorial

    Graph Laplacian Matrix Calculator Enter Undirected Edges (u v) one per line: Laplacian Type: Combinatorial L = D – ANormalized L̃ = D⁻½ L D⁻½ Calculate Laplacian Matrix * Based on L = D – A (combinatorial) or L̃ = D⁻½ L D⁻½ (normalized). Eigenvalues reveal connectivity and clustering. About the Graph Laplacian

    Strongly Connected Component Finder Enter Directed Edges (u -> v) one per line: Algorithm: Kosaraju’s AlgorithmTarjan’s Algorithm Find Strongly Connected Components * Based on Kosaraju’s (DFS twice) and Tarjan’s (single DFS with low-link) algorithms. SCCs are maximal sets with paths in both directions. About the Strongly Connected Component Finder The Strongly Connected Component

    Graph Connectivity Checker Enter Edges (u v) one per line: Analysis Method: DFS (Depth-First Search)BFS (Breadth-First Search)Union-Find (Disjoint Set)Menger’s Theorem (k-Connectivity) Check Graph Connectivity * Based on DFS/BFS traversal, Union-Find, and Menger’s theorem. A graph is connected if one component exists. About the Graph Connectivity Checker The Graph Connectivity Checker is a robust

    Ramsey Number Estimator Clique Size s (≥3): Independent Set Size t (≥3): Estimate Ramsey Number * Based on Ramsey’s theorem, probabilistic lower bounds, and known exact values. R(3,3)=6, R(5,5) ∈ [43,48]. About the Ramsey Number Estimator The Ramsey Number Estimator is a graph-theoretic tool that computes known bounds for the Ramsey number R(s,t)