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Dong, F. M.
Preferred name
Dong, F. M.
Email
fengming.dong@nie.edu.sg
Department
Mathematics & Mathematics Education (MME)
Personal Site(s)
ORCID
51 results
Now showing 1 - 10 of 51
- PublicationOpen AccessSome inequalities on chromatic polynomials(New Zealand Mathematical Society, 2001)
; ;Teo, Kee Leong ;Little, Charles H. C.Hendy, MichaelFor a given graph G, let P (G , A) be the chromatic polynomial of G, where A is considered to be a real number. In this paper, we study the bounds for P (G , A )/P (G , A — 1) and P (G , A )/P (G - x, A), where x is a vertex in G, A > n and n is the number of vertices of G.181 273 - PublicationOpen AccessMathematical problem solving for integrated programme students(2006-05)
; ;Quek, Khiok Seng; ;Lee, Tuo Yeong ;Lim-Teo, Suat Khoh; Ho, Foo Him166 311 - PublicationOpen AccessGraph-functions associated with an edge-property(Combinatorial Mathematics Society of Australasia, 2004)
; ;Hendy, Michael ;Teo, Kee LeongLittle, Charles H. C.Let P be an edge-property of graphs. For any graph G we construct a polynomial Ψ(G, η,P), in an indeterminate η, in which the coefficient of ηr for any r ≥ 0 gives the number of subsets of E(G) that have cardinality r and satisfy P. An example is the well known matching polynomial of a graph. After studying the properties of Ψ(G, η,P) in general, we specialise to two particular edge-properties: that of being an edge-covering and that of inducing an acyclic subgraph. The resulting polynomials, called the edge-cover and acyclic polynomials respectively, are studied and recursive formulae for computing them are derived. As examples we calculate these polynomials for paths and cycles.168 145 - PublicationOpen AccessChromatic roots of a ring of four cliquesFor any positive integers a, b, c, d, let Ra,b,c,d be the graph obtained from the complete graphs Ka,Kb,Kc and Kd by adding edges joining every vertex in Ka and Kc to every vertex in Kb and Kd. This paper shows that for arbitrary positive integers a, b, c and d, every root of the chromatic polynomial of Ra,b,c,d is either a real number or a non-real number with its real part equal to (a + b + c + d − 1)/2.
174 148 - PublicationOpen AccessTwo invariants for adjointly equivalent graphs(Combinatorial Mathematics Society of Australasia, 2002)
; ;Teo, Kee Leong ;Little, Charles H. C.Hendy, MichaelTwo graphs are defined to be adjointly equivalent if their complements are chromatically equivalent. We study the properties of two invariants under adjoint equivalence.204 156 - PublicationOpen AccessReading mathematics: A holistic curriculum approach(2017-07)
; ; ; ;Yap, Romina Ann Soon; ; ; ;Cheang, Wai Kwong; ; ; Quek, Khiok Seng393 262 - PublicationEmbargoOn the maximum local mean order of sub-k-trees of a k-treeFor a κ-tree T, a generalization of a tree, the local mean order of sub-κ-trees of T is the average order of sub-κ-trees of T containing a given κ-clique. The problem whether the maximum local mean order of a tree (i.e., a 1-tree) at a vertex is always taken on at a leaf was asked by Jamison in 1984 and was answered by Wagner and Wang in 2016. Actually, they proved that the maximum local mean order of a tree at a vertex occurs either at a leaf or at a vertex of degree 2. In 2018, Stephens and Oellermann asked a similar problem: for any κ-tree T, does the maximum local mean order of sub-κ-trees containing a given κ-clique occur at a κ-clique that is not a major κ-clique of T? In this paper, we give it an affirmative answer.
21 77 - PublicationEmbargoComparing list-color functions of uniform hypergraphs with their chromatic polynomials (ii)
For any r-uniform hypergraph H with m (≥ 2) edges, let P(H, k) and Pl(H, k) be the chromatic polynomial and the list-color function of H respectively, and let ρ(H) denote the minimum value of |e \ e′| among all pairs of distinct edges e, e′ in H. We will show that if r ≥ 3, ρ(H) ≥ 2 and m ≥ ρ(H)3/2 +1, then Pl(H, k) = P(H, k) holds for all integers k ≥ 2.4(m−1) / ρ(H) log(m−1).
24 79 - PublicationOpen AccessOn graphs whose flow polynomials have real roots onlyLet G be a bridgeless graph. In 2011 Kung and Royle showed that all roots of the ow polynomial F(G; ) of G are integers if and only if G is the dual of a chordal and plane graph. In this article, we study whether a bridgeless graph G for which F(G; ) has real roots only must be the dual of some chordal and plane graph. We conclude that the answer of this problem for G is positive if and only if F(G; ) does not have any real root in the interval (1; 2). We also prove that for any non-separable and 3-edge connected G, if G - e is also non-separable for each edge e in G and every 3-edge-cut of G consists of edges incident with some vertex of G, then all roots of P(G; ) are real if and only if either G 2 fL;Z3;K4g or F(G; ) contains at least 9 real roots in the interval (1; 2), where L is the graph with one vertex and one loop and Z3 is the graph with two vertices and three parallel edges joining these two vertices.
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