The chromatic polynomial of grid graph P3□Pn

This paper studies the chromatic polynomial of some special graphs like path graph, ladder graph and grid graph using the concept of digonalization of transfer matrix to solve simultaneous recurrence relation. The aim of this paper is to solve an open problem on the chromatic polynomial of grid graph (Problem 8.1 of Selected Topics in Graph Theory , Volume 3 which is edited by Lowell W. Beineke and Robin J. Wilson) and give general formula of the chromatic polynomial in λ of grid graph P 3 □ P n , where n ∈ N without any condition on n where λ denotes number of available colors.