Knighted!

A graph with 64 nodes represents the squares of a chessboard. The nodes are joined appropriately by edges, each representing a move of the knight. In this graph, every node will be of degree two, three, four, six, or eight. Let the values \(a,b,c,d\) and \(e\) be the number of nodes with each respective degree such that \(a\) is the number of nodes with degree two, \(b\) is the number of nodes with degree three, etc. What is the value of \(a+c+e?\)

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