- Dong Fengming

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# Dong Fengming

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Dong Fengming

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fengming.dong@nie.edu.sg

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Mathematics & Mathematics Education (MME)

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- PublicationOpen AccessZeros of adjoint polynomials of paths and cycles(2002)
; ;Teo, Kee Leong ;Little, Charles H. C.Hendy, MichaelShow more The chromatic polynomial of a simple graph G with n > 0 vertices is a polynomial Σnk =1α(G, k)(x)k of degree n, where (x)k = x(x−1) . . . (x−k+1) and α(G, k) is real for all k. The adjoint polynomial of G is defined to be Σnk=1α(G, k)μk, where G is the complement of G. We find the zeros of the adjoint polynomials of paths and cycles.Show more 352 99 - PublicationOpen AccessChromatically unique multibridge graphs(2004)
; ;Teo, Kee Leong ;Little, Charles H. C. ;Hendy, MichaelKoh, Khee MengShow more Let (a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ (a1, a2, · · · , ak) is chromatically unique if ak < a1 +a2, and find examples showing that θ (a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.Show more 215 73 - PublicationOpen AccessTwo invariants for adjointly equivalent graphs(2002)
; ;Teo, Kee Leong ;Little, Charles H. C.Hendy, MichaelShow more Two graphs are defined to be adjointly equivalent if their complements are chromatically equivalent. We study the properties of two invariants under adjoint equivalence.Show more 184 65 - PublicationOpen AccessLower bound on the weakly connected domination number of a cycledisjoint graph(2010)
;Koh, Khee Meng ;Ting, T. S. ;Xu, Z. L.Show more For a connected graph G and any non-empty S ⊆ V (G), S is called a weakly connected dominating set of G if the subgraph obtained from G by removing all edges each joining any two vertices in V (G) \ S is connected. The weakly connected domination number γw(G) is defined to be the minimum integer k with |S| = k for some weakly connected dominating set S of G. In this note, we extend a result on the lower bound for the weakly connected domination number γw(G) on trees to cycle-e-disjoint graphs, i.e., graphs in which no cycles share a common edge. More specifically, we show that if G is a connected cycle-e-disjoint graph, then γw(G) ≥ (|V (G)| − v1(G) − nc(G) − noc(G) + 1)/2, where nc(G) is the number of cycles in G, noc(G) is the number of odd cycles in G and v1(G) is the number of vertices of degree 1 in G. The graphs for which equality holds are also characterised.Show more 142 73 - PublicationOpen AccessReading mathematics: A holistic curriculum approach(2017-07)
; ; ; ;Yap, Romina Ann Soon; ; ; ;Cheang, Wai Kwong; ; ; Quek, Khiok SengShow more 372 162 - PublicationOpen AccessSome inequalities on chromatic polynomials(2001)
; ;Teo, Kee Leong ;Little, Charles H. C.Hendy, MichaelShow more For 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.Show more 115 157 - PublicationOpen AccessA characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set(2012)
;Koh, Khee Meng ;Ting, T. S.Show more Let G be a connected graph with vertex set V (G). A set S of vertices in G is called a weakly connected dominating set of G if (i) S is a dominating set of G and (ii) the graph obtained from G by removing all edges joining two vertices in V (G) \ S is connected. A weakly connected dominating set S of G is said to be minimum or a γw-set if |S| is minimum among all weakly connected dominating sets of G. We say that G is γw-unique if it has a unique γw-set. Recently, a constructive characterisation of γw-unique trees was obtained by Lemanska and Raczek [Czechoslovak Math. J. 59 (134) (2009), 95–100]. A graph is said to be cycle-disjoint if no two cycles in G have a vertex in common. In this paper, we extend the above result on trees by establishing a constructive characterisation of γw-unique cycle-disjoint graphs.Show more 116 81 - PublicationOpen Access
367 101 - PublicationOpen AccessGraph-functions associated with an edge-property(2004)
; ;Hendy, Michael ;Teo, Kee LeongLittle, Charles H. C.Show more 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.Show more 131 59 - PublicationOpen AccessMathematical problem solving for integrated programme students(2006-05)
; ;Quek, Khiok Seng; ;Lee, Tuo Yeong ;Lim-Teo, Suat Khoh; Ho, Foo HimShow more 143 189