Short Lecture Series: Graph Theory Basics (≈1 minute each)

Overview

Three concise visual lessons for 11th‑grade students introducing (1) what a graph is, (2) Euler vs. Hamilton paths, and (3) the shortest‑path problem with Dijkstra’s algorithm. Each segment uses familiar network diagrams (city road map and a simple social‑media friendship graph) to make the concepts intuitive.

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Phases

#	Phase Name	Duration	Description
1	Graph Definition	~18 s	Introduce vertices and edges, show a real‑world road‑network diagram, label a few vertices (cities) and edges (roads).
2	Euler vs. Hamilton	~22 s	Present two small graphs side‑by‑side: one with an Eulerian trail (drawn over all edges once) and one with a Hamiltonian path (drawn over all vertices once). Highlight the difference with colour and brief visual cue.
3	Shortest Path & Dijkstra	~20 s	Animate Dijkstra’s algorithm on a weighted city map, gradually fixing the shortest distances from a start city to all others, ending with the shortest route to a target city.
4	Outro Summary	~5 s	Fade‑in three bullet icons summarizing the key takeaways (definition, path types, shortest‑path algorithm).

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Layout

┌─────────────────────────────────────────────┐
│                TITLE / TOPIC                │
├──────────────────────┬──────────────────────┤
│   MAIN VISUAL (GRAPH)│   SUPPORT (labels,   │
│                      │   short equations)   │
├──────────────────────┴──────────────────────┤
│            BOTTOM CAPTION / NOTES          │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title that changes per phase (e.g., "What is a Graph?", "Euler vs. Hamilton", "Dijkstra's Shortest Path").	Fades in at the start of each phase.
Left	Central diagram: road‑network or social‑graph, animated to illustrate the concept of the current phase.	Primary focus; occupies ~60 % of width.
Right	Supporting visual aids: small legends, edge‑weight numbers, or brief symbolic arrows indicating traversal direction.	Keeps the left side uncluttered; appears with a gentle slide‑in.
Bottom	Very short caption (≤10 words) summarizing the step, e.g., "All edges visited once" or "Current shortest distance = 7 km".	Small font, fades in with the left diagram.

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Notes

• Keep total runtime under 1 minute 30 seconds; each phase is timed to fit within that budget.
• Use a consistent colour palette: vertices – teal, edges – gray, traversed edges – orange, highlighted path – green.
• No on‑screen paragraph text; rely on visual labels and brief captions.
• Transitions between phases are simple cross‑fades (≈0.5 s) to maintain flow.
• The final outro uses three simple icons (a node, a looped arrow, and a lightning bolt) to reinforce the three concepts.