Yee-Hock Peng

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The graph consisting of s paths joining two vertices is called an s-bridge graph. In this paper, we discuss the chromaticity of some families of s-bridge graphs, especially 4-bridge graphs, and some graphs related to s-bridge graphs. 1. The chromaticity of 4-bridge graphs The graphs considered here are finite, undirected, simple and loopless. For a graph G,(More)
Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, if P(G) = P(H). A set of graphs S is called a chromatic equivalence class if for any graph H that is chromatically equivalent with a graph G in S, then H ∈S. Peng et al. (Discrete Math. 172 (1997) 103–114), studied the chromatic equivalence classes of(More)
Let G V, E be a simple graph. A set S ⊆ V is a dominating set of G, if every vertex in V \S is adjacent to at least one vertex in S. Let Pi n be the family of all dominating sets of a path Pn with cardinality i, and let d Pn, j |P n|. In this paper, we construct Pi n, and obtain a recursive formula for d Pn, i . Using this recursive formula, we consider the(More)
Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G∼H , if P(G) = P(H). A graph G is chromatically unique if for any graph H , G∼H implies that G is isomorphic with H . In this paper, we give the necessary and su:cient conditions for a family of generalized polygon trees to be chromatically(More)
and Applied Analysis 3 P2 For t ∈ 0, T , the resolvent R λ,A t of A t exists for all λ with Reλ ≤ 0 and there exists a constant M > 0 such that ‖R λ,A t ‖£ X ≤ M |λ| 1 , for t ∈ 0, T . 2.1 P3 There exist constants L > 0 and 0 < α ≤ 1 such that ∥∥ A t −A s A−1 τ ∥∥ £ X ≤ L|t − s| for s, t, τ ∈ 0, T . 2.2 Let X1 {D, ‖ · ‖1} where ‖x‖1 ‖Ax‖. X1 is a Banach(More)
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