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A House graph with equal degrees

Source: IMOC 2021 C4

August 11, 2021
combinatoricsgraph theoryIMOC2021

Problem Statement

There is a city with many houses, where the houses are connected by some two-way roads. It is known that for any two houses A,BA,B, there is exactly one house CC such that both A,BA,B are connected to CC. Show that for any two houses not connected directly by a road, they have the same number of roads adjacent to them.
ST