Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j) : 1

Question

Consider an undirected graph G where self-loops are not allowed. The vertex set of G is {(i, j) : 1 <= i <= 12, 1 <= j <= 12}. There is an edge between (a, b) and (c, d) if |a - c| <= 1 and |b - d| <= 1. The number of edges in this graph is ______.

Accepted Answer

506 The vertex set is a 12x12 grid. Two vertices (a,b) and (c,d) are adjacent when they differ by at most 1 in each coordinate — i.e., they are horizontal, vertical, or diagonal neighbours in the grid (like a king's moves in chess). We count all such pairs (excluding self-loops).