Total weight is the sum of the weights assigned to the edges in a weighted graph. It is used to evaluate the overall cost or distance of traversing all edges in a specific path or cycle.
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In Hamilton cycles, total weight represents the sum of all edge weights in the cycle.
Calculating total weight helps determine the efficiency of different Hamiltonian paths.
The goal often involves finding a Hamilton cycle with the minimum total weight, known as the Traveling Salesman Problem (TSP).
Total weight can vary significantly depending on which edges and vertices are included in the cycle.
Graphs can be weighted positively, negatively, or mixed, impacting how total weight is calculated and interpreted.
Review Questions
What does total weight represent in a weighted graph?
Why is calculating total weight important when analyzing Hamilton cycles?
How does varying edge weights impact the calculation of total weight?
Related terms
Weighted Graph: A graph where each edge has an associated numerical value or weight
Hamilton Cycle: A cycle that visits every vertex exactly once and returns to the starting vertex
Traveling Salesman Problem (TSP): An optimization problem that seeks to find the shortest possible route visiting each city and returning to the origin city