Let's compare the games in Figures \(A\) and \(B\). In the game Diamonds, shown in Figure \(A\), each player begins in the space marked START and proceeds in a counterclockwise direction. On each turn, the player rolls a six-sided die and moves forward the number of spaces shown on the die. If the player lands on a space marked with a diamond, the player jumps to the next space marked with a diamond and stops there. The first player to land in or pass the space marked END wins. In the Dots game, shown in Figure \(B\), each player begins in the space marked 1 and proceeds in numerical order through the numbered spaces. On each turn, the player rolls a sixsided die and moves forward the number of spaces shown on the die. When a player lands on a space marked with a green dot, they immediately move to the space indicated by the arrow. Construct a graph to represent each gameboard such that each vertex represented a space on the game board and each edge represented the ability of a player to move directly from one space to the next. For example, in the Dots game, the vertex representing space 3 would be adjacent to 2, 4, and 6 . Identify at least three differences between a graph based on Diamonds and a graph based on Dots to show the graphs are not isomorphic.

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START END Figure A Diamond game Two Game Boards 1 8 00 9 16 2 7 10 15 3 6 11 14 st 4 5 12 13 Figure B Dots game