Previous research has found a number of order and size of graph horse step on the chessboard of size and as a whole. However, not determined how many horse step on every box of chess with search of all possibilities. So, in this research, the writer are interested in researching how to determine the number of horse step at the chessboard size , from the perspective of many facets of their respective pieces, which aims to determine the number of horse step of the box of chessboard size . The steps used in this research is to draw a chessboard, laying knight on any one box on chessboard, counting the number of horse step in each box in turn, finding for patterns, determine theorem, then prove theorem given. Graf used in this research is which defined as a pair between point and side with a set of not empty point and finite, and the pair of not ordered edge which my be empty. Therefore, this graph is limited at graph which has set of finite points and graph which has not double edge (loop). Based on the discussion results obtained a theorem which states that the possible number of horse step in each box of the chess board size , and , is generally obtained by the possibility of two conditions, namely:
1. For ; ; ;
2. For ; ;
;
with and ;
with and and
; and .
As it is known that this research only involved one knight, it is suggested for further
research to examine the possibility that happen in other pieces, can also be equipped with a
simulation using a computer program, to be easier to determine the number of horse step in
each box chess.
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