TY - JOUR
T1 - On properties of adjoint polynomials of graphs and their applications
AU - Zhao, Haixing
AU - Liu, Ruying
AU - Li, Xueliang
AU - Wang, Ligong
PY - 2004
Y1 - 2004
N2 - For a graph G, we denote by P(G, λ) the chromatic polynomial of G and by h(G, x) the adjoint polynomial of G. A graph G is said to be chromatically unique if for any graph H, P(H, λ) = P(G, λ) implies H ≅ G. In this paper, we investigate some algebraic properties of the adjoint polynomials of some graphs. Using these properties, we obtain necessary and sufficient conditions for Kn - E(∪a,bT1,a,b) and (∪iCni) ∪ (∪iDmj) ∪ (∪a,bT1,a,b) to be chromatically unique if Gi ∈ {Cn,Dn, T1,a,b|n ≥ 5, 3 ≤ a ≤ 10, a ≤ b} and h(Pm) h(Gi) for all m ≥ 2. Moreover, many new chromatically unique graphs are given.
AB - For a graph G, we denote by P(G, λ) the chromatic polynomial of G and by h(G, x) the adjoint polynomial of G. A graph G is said to be chromatically unique if for any graph H, P(H, λ) = P(G, λ) implies H ≅ G. In this paper, we investigate some algebraic properties of the adjoint polynomials of some graphs. Using these properties, we obtain necessary and sufficient conditions for Kn - E(∪a,bT1,a,b) and (∪iCni) ∪ (∪iDmj) ∪ (∪a,bT1,a,b) to be chromatically unique if Gi ∈ {Cn,Dn, T1,a,b|n ≥ 5, 3 ≤ a ≤ 10, a ≤ b} and h(Pm) h(Gi) for all m ≥ 2. Moreover, many new chromatically unique graphs are given.
UR - http://www.scopus.com/inward/record.url?scp=67349103265&partnerID=8YFLogxK
M3 - 文章
AN - SCOPUS:67349103265
SN - 1034-4942
VL - 30
SP - 291
EP - 306
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
ER -