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Dong Fengming
Preferred name
Dong Fengming
Email
fengming.dong@nie.edu.sg
Department
Mathematics & Mathematics Education (MME)
Personal Site(s)
ORCID
47 results
Now showing 1 - 10 of 47
- PublicationOpen AccessMathematical problem solving for integrated programme students(2006-05)
; ;Quek, Khiok Seng; ;Lee, Tuo Yeong ;Lim-Teo, Suat Khoh; Ho, Foo Him145 233 - PublicationOpen Access
371 117 - PublicationOpen AccessOn graphs having no flow roots in the Interval (1, 2)(2015)For any graph G, let W(G) be the set of vertices in G of degrees larger than 3. We show that for any bridgeless graph G, if W(G) is dominated by some component of G-W(G), then F(G,λ ) has no roots in (1; 2), where F(G,λ ) is the flow polynomial of G. This result generalizes the known result that F(G,λ ) has no roots in (1, 2) whenever |W(G)| ≤2. We also give some constructions to generate graphs whose flow polynomials have no roots in (1, 2).
128 89 - PublicationOpen AccessA characterisation of cycle-disjoint graphs with unique minimum weakly connected dominating set(2012)
;Koh, Khee Meng ;Ting, T. S.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.120 95 - PublicationOpen AccessGraph-functions associated with an edge-property(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. - PublicationOpen AccessChromatic roots of a ring of four cliques(2011)
; ;Royle, GordonWagner, DaveFor 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)/2.156 69 - PublicationOpen AccessReading mathematics: A holistic curriculum approach(2017-07)
; ; ; ;Yap, Romina Ann Soon; ; ; ;Cheang, Wai Kwong; ; ; Quek, Khiok Seng374 177 - PublicationOpen AccessTwo invariants for adjointly equivalent graphs(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.186 79 - PublicationOpen AccessUpper bounds on the signed edge domination number of a graph(2021)
; ;Ge, JunYang, YanA signed edge domination function (or SEDF) of a simple graph G=(V,E) is a function f:E→{1,−1} such that ∑e′∈N[e]f(e′)≥1 holds for each edge e∈E, where N[e] is the set of edges in that share at least one endpoint with e. Let γs′(G) denote the minimum value of f(G) among all SEDFs f, where f(G)=∑e∈Ef(e). In 2005, Xu conjectured that γs′(G)≤n−1, where n is the order of G. This conjecture has been proved for the two cases vodd(G)=0 and veven(G)=0, where vodd(G) (resp. veven(G)) is the number of odd (resp. even) vertices in G. This article proves Xu’s conjecture for veven(G)∈{1,2}. We also show that for any simple graph G of order n, γs′(G)≤n+vodd(G)∕2 and γs′(G)≤n−2+veven(G) when veven(G)>0, and thus γs′(G)≤(4n−2)∕3. Our result improves the best current upper bound of γs′(G)≤⌈3n∕2⌉.WOS© Citations 2 69 33Scopus© Citations 2 - PublicationOpen AccessOn the sizes of bipartite 1-planar graphs(2021)
; ;Huang, YuanqiuOuyang, ZhangdongA graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let G be a bipartite 1-planar graph with n (n ≥4) vertices and m edges. Karpov showed that m ≤ 3n - 8 holds for even n ≥ 8 and m ≤3n - 9 holds for odd n ≥ 7. Czap, Przybylo and Škrabul’áková proved that if the partite sets of G are of sizes x and y, then m ≤ 2n+6x-12 holds for 2 ≤ x ≤ y, and conjectured that m ≤ 2n + 4x - 12 holds for x ≥ 3 and y ≥ 6x - 12. In this paper, we settle their conjecture and our result is even under a weaker condition 2 ≤ x ≤ y.WOS© Citations 1Scopus© Citations 1 265 35