Graph Theory Math Ia Link

Current = S (distance 0). Neighbors: A(200), B(350). Update: A=200, B=350. Visited = S.

1. Introduction Aim: To determine the most efficient (shortest) route for a delivery driver in a local suburban network using graph theory, and to compare the effectiveness of Dijkstra’s algorithm against simple visual inspection.

Unvisited min = C(530). Current = C. Neighbors: A(no), B(no), D(no), E(530+250=780 vs 630 no). Visited S,A,B,D,C. graph theory math ia

Unvisited min = E(630). Current = E. Neighbors: B(no), C(no), F(630+100=730 vs 810 → update F=730). Visited add E.

(sort edges by weight, add if no cycle): Current = S (distance 0)

I defined terms clearly, used consistent notation (( G=(V,E) )), and showed step-by-step tables.

Unvisited min = F(730). Current = F. Neighbors: D(no), E(no), T(730+90=820 vs 1010 → update T=820). Visited add F. Visited = S

Unvisited min = D(510). Current = D. Neighbors: A(no), B(no), C(510+120=630 vs 530 no), F(510+300=810), T(510+500=1010). Update T tentative = 1010. Visited S,A,B,D.

| Edge | Weight | Edge | Weight | |------|--------|------|--------| | S–A | 200 | B–C | 180 | | S–B | 350 | C–D | 120 | | A–B | 150 | C–E | 250 | | A–C | 400 | D–F | 300 | | B–D | 220 | E–F | 100 | | B–E | 280 | F–T | 90 | | A–D | 310 | D–T | 500 (direct but long) |

Destination T reached (820). Stop.

I used Google Maps for weights and could extend to Excel/Python.