Abstract
In this paper it is proved that if the chromatic polynomial P( G; λ) is maximum for λ = 3 in the class of 3-chromatic 2-connected graphs G of order n, then G is isomorphic to the graph consisting of C 4 and C n−1 , having in common a path of length two for every even n ⩾ 6. This solves a conjecture raised in (Tomescu, 1994). Also, the fourth maximum chromatic polynomial P( G; λ) for λ = 3 in the class of 2-connected graphs of order n and all extremal graphs are deduced for every n ⩾ 5.
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