GraphQuest: Exploring the Logic of Links
An Experiential Bootcamp on Graph Theory and Connectivity

In the spirit of how mathematics has always grown through patterns, connections, and careful reasoning – GraphQuest is designed as a 20-hour immersive bootcamp that brings the foundational ideas of Graph Theory to life. From the earliest problems of bridges and routes to today’s networks and algorithms, graphs have long been a quiet backbone of logical thinking. This bootcamp honours that tradition while presenting it in a way that feels hands-on, relevant, and engaging.

Serving as a formative assessment, GraphQuest focuses on strengthening students’ understanding of basic graph-theoretic concepts through exploration, discussion, and guided practice. Instead of treating assessment as a final checkpoint, this bootcamp treats learning as a journey where mistakes are part of the process and connections slowly click into place. Learners actively build, analyse, and interpret graphs to demonstrate their growing command over ideas such as vertices, edges, paths, cycles, and connectivity.

Across 20 structured hours, participants will move from intuitive, real-world linkages to formal mathematical representations, blending time-tested methods of problem-solving with interactive activities. The goal is simple but powerful: to ensure that every learner not only knows the definitions of Graph Theory, but truly gets how and why these ideas work. Think of it as old-school rigor, but with modern energy – focused, practical, and low-key exciting.

Task 1: Visual Graph Dictionary – “See the Shape of Logic”

Topics: Simple, Complete, Bipartite, Regular Graphs
Activity:
Each team creates a digital gallery of graph types using hand-drawn sketches or NetworkX visuals, labeling nodes, edges, and degrees.
Learning Outcome: Identify and classify different types of graphs and relate visual structures to definitions.
Deliverable: Visual collage or PPT poster of at least 6 graph types with short captions.

Task 2: Build Your Own Graph – “Nodes of Reality”

Topics: Directed, Undirected, Weighted Graphs
Activity: Pick a real-world situation (Instagram followers, road network, WhatsApp chats etc.) and model it as a graph.
Learning Outcome: Apply graph theory concepts to model real-world relationships.
Deliverable: Graph diagram + explanation of why edges are directed/undirected.

Task 3: Degree Detective – “Count the Connections”

Topics: Incidence, Degree, Pendant, Isolated Vertices
Activity: Construct small graphs and manually compute degrees of each vertex, identifying pendant and isolated vertices.
Learning Outcome: Calculate vertex degrees and interpret graph connectivity.
Deliverable: Tabular representation of degrees and classification of vertices.

Task 4: The Null Network – “When Nothing Connects”

Topics: Null Graphs, Incidence Matrix, Adjacency Matrix
Activity: Visualize graphs and derive their incidence and adjacency matrices using Python / Excel.
Learning Outcome: Translate visual graph structure into matrix form.
Deliverable: Matrix representation + reflection on how it encodes edge information.

Task 5: Operation Lab – “Mix, Merge, and Modify”

Topics: Graph operations (Union, Intersection, Ring sum, Decomposition, Fusion)
Activity: Perform operations on two small graphs and observe how edges and vertices change.
Learning Outcome: Analyze results of graph operations and identify their use cases.
Deliverable: Step-by-step comparison table and visual before/after diagrams.

Task 6: Pathfinder Challenge – “Find Your Way”

Topics: Walk, Path, Circuit
Activity: Design an activity to trace all possible walks/paths/circuits between two given vertices on a hand-drawn or generated graph.
Learning Outcome: Distinguish between walks, paths, and circuits; apply traversal logic.
Deliverable: Path tracing worksheet + shortest-path identification.

Task 7: Isomorphism Hunt – “Different Looks, Same Logic”

Topics: Graph Isomorphism
Activity: Draw all possible simple graphs on 2/3/4 vertices and prove or disprove isomorphism through degree sequences and adjacency matrices.
Learning Outcome: Verify graph isomorphism through structural comparison.
Deliverable: Written proof + supporting diagrams.

Task 8: Compiler Dependency Map – “Code Connections”

Topics: Subgraphs, Connected Components
Activity: Represent modules or classes of a small software project as a graph, where edges represent dependencies or imports. Identify isolated modules and strongly connected subgraphs.
Learning Outcome: Analyze software architecture using graph-theoretic methods.
Deliverable: Dependency graph diagram + list of isolated or tightly coupled modules.

 Task 9: Web Crawler Graph – “From Links to Networks”

Topics: Directed Graphs, Connectivity
Activity: Simulate a web crawler: represent a small set of websites (pages) and their links as a directed graph. Analyze if the graph is strongly connected.
Learning Outcome: Relate graph connectivity to web structure and information flow.
Deliverable: Python notebook + visual representation of site linking.

Task 10: GraphVerse – “Connecting All the Connections”

Activity: Higher Order Thinking Challenge

Description: To enhance analytical and evaluative thinking, each team must create 5 Higher Order Thinking (HOTS) questions covering the full set of graph theory topics learned.

Instructions:

• Develop 5 higher-order thinking questions.
• Each question must align with Bloom’s higher cognitive levels (Apply, Analyze, Evaluate, Create).
• Include real-world applications, ethical perspectives, and creative problem-solving.
• Encourage inter‑topic integration (e.g., connectivity + isomorphism + real‑world networks).

Deliverables:

• A document or slide deck with 5 HOTS questions.
• Each question labeled with its Bloom’s cognitive level.
• (Optional) Include key points or a model answer for peer learning.

Learning Outcomes:

• Apply higher‑order reasoning to graph theory concepts.
• Demonstrate critical and creative thinking.
• Connect theory to real‑world computational and ethical scenarios.
• Strengthen academic discussion and leadership skills.