Chromatic Classes of 2-Connected(n,n+4)-Graphs with Exactly Three Triangles and at Least Two Induced 4-Cycles

摘要

For a graphG, letP(G,λ)be its chromatic polynomial. Two graphsGandHare chromatically equivalent, denotedG~H, ifP(G,λ)=P(H,λ). A graphGis chromatically unique ifP(H,λ)=P(G,λ)implies thatH≅G. In this paper, we determine all chromatic equivalenceclasses of 2-connected (n,n+4)-graphs with exactly three triangles and at least two induced 4-cycles. As a byproduct of these, we obtain various new families ofχ-equivalent graphs andχ-unique graphs.