# zbMATH — the first resource for mathematics

Adjoint polynomials and chromatically unique graphs. (English) Zbl 0878.05030
This paper surveys some results about chromatically unique graphs obtained studying their adjoint polynomials.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
chromatic unique; adjoint polynomial; chromatic polynomial
Full Text:
##### References:
 [1] Biggs, N., () [2] Bondy, J.A.; Murty, U.S.R., () [3] Chao, C.Y.; Whitehead, E.G., On chromatic equivalence of graphs, (), 121-131 [4] Du, Q.Y., On σ-polynomials and a class of chromatically unique graphs, Discrete math., 115, 153-165, (1993) · Zbl 0774.05039 [5] Farrell, E.J., An introduction to matching polynomials, J. combin. theory (B), 27, 75-86, (1979) · Zbl 0335.05131 [6] Guo, Z.-Y.; Li, Y.-J., Chromatic uniqueness of complement of the cycles union, Kexue tongbao, 33, 1676, (1988) [7] Koh, K.M.; Teo, K.L., The search for chromatically unique graphs, Graphs combin., 6, 259-285, (1990) · Zbl 0727.05023 [8] Korfhage, R., Σ-polynomials and graph coloring, J. combin. theory (B), 24, 137-153, (1978) · Zbl 0845.05043 [9] Li, N.Z.; Whitehead, E.G.; Xu, S.J., Classification of chromatically unique graphs having quadratic σ-polynomials, J. graph theory, 11, 169-176, (1987) · Zbl 0686.05021 [10] Li, N.Z., On graphs having σ-polynomials of the same degree, Discrete math., 110, 185-196, (1992) · Zbl 0771.05038 [11] Liu, R.-Y., A new method to find chromatic polynomial of graph and its applications, Kexue tongbao, 32, 1508-1509, (1987) [12] Liu, R.-Y., On chromatic polynomials of two classes of graphs, Kexue tongbao, 32, 1147-1148, (1987) [13] Liu, R.-Y., On chromatic polynomials of complementary graphs of trees, J. xinjiang university, 6, 6-8, (1989) · Zbl 1056.05501 [14] Liu, R.-Y., Adjoint polynomial of graphs, J. qinghai normal university, 8, 3, 1-9, (1990) [15] Liu, R.-Y., Chromatic uniqueness of $$Kn − E(kPs ⊎ rPt)$$, J. systems sci. math. sci., 12, 207-214, (1992) [16] Liu, R.-Y., Several results on adjoint polynomials of graphs, J. qinghai normal university, 10, 1-6, (1992) [17] Liu, R.-Y., On the irreducible graphs, J. qinghai normal university, 11, 4, 29-33, (1993) [18] Liu, R.-Y., Chromatic uniqueness of complementary graph of Pq − 1, J. math. res. exposition, 14, 469-472, (1994) · Zbl 0882.05066 [19] Liu, R.-Y., Chromatic uniqueness of a kind of graph, J. neimenggu university, 25, 469-475, (1994) · Zbl 1333.05118 [20] Liu, R.-Y., Chromatic uniqueness of complement of the irreducible cycles union, Math. appl., 7, 200-205, (1994) [21] Liu, R.-Y., Chromatic uniqueness of complementary graphs of a kind of trees, Math. applicata supplement, 9, 170-173, (1996) [22] Liu, R.-Y.; Bao, X.-W., Chromatic uniqueness of the complements of 2-regular graphs, Pure appl. math. suppl, 9, 2, 69-71, (1993) [23] Liu, R.-Y., Two new classes of chromatically unique graphs, J. neimenggu university, 27, 11-17, (1996) · Zbl 1268.05080 [24] Liu, R.-Y.; Li, N.-Z., Chromatic uniqueness of a kind of graph of the Kn − E(G) type, Acta math. scientia, 14, 316-320, (1994) [25] Liu, R.-Y.; Wang, J.-F., On chromatic uniqueness of complement of union of cycles and paths, Theoret. comput. sci., 1, 112-126, (1992) [26] Read, R.C., An introduction to chromatic polynomials, J. combin. theory, 4, 52-71, (1968) · Zbl 0173.26203 [27] Xu, S.J., On σ-polynomials, Discrete math., 69, 189-194, (1988) · Zbl 0658.05025 [28] Ye, C.-F.; Liu, R.-Y., Chromatic uniqueness of a new family of graphs, Pure appl. math., 10, 46-53, (1994), (special issue) [29] Frucht, R.W., A new method of computing chromatic polynomials of graphs, Lecture notes in pure appl. math., Vol. 96, 69-77, (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.