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Shao Z.,Sichuan University | Shao Z.,Institutions of Higher Education of Sichuan Province | Xu J.,Peking University | Yeh R.K.,Feng Chia University
Journal of Combinatorial Optimization | Year: 2016

Let G = (V, E) be a graph. Denote dG(u, v) the distance between two vertices u and v in G. An L(2, 1)-labeling of G is a function f: V → {0, 1, ⋯} such that for any two vertices u and v, |f(u) - f(v)| ≥ 2 if dG(u, v)=1 and |f(u) - f(v)| ≥ 1 if dG(u, v)=2. The span of f is the difference between the largest and the smallest number in f(V). The λ-number of G, denoted λ(G), is the minimum span over all L(2, 1)-labelings of G. In this article, we confirm Conjecture 6.1 stated in X. Li et al. (J Comb Optim 25:716–736, 2013) in the case when (i) ℓ is even, or (ii) ℓ ≥ 5 is odd and 0 ≤ r≤ 8. © 2014, Springer Science+Business Media New York. Source


Zhang X.,Sichuan University | Zhang X.,Institutions of Higher Education of Sichuan Province
Journal of Computational and Theoretical Nanoscience | Year: 2014

An L(d,1)-labeling for a graph G is a function f : V (G)→{0,1, } such that f (u)?f (v) ≥ d whenever uv ε E(G) and f (u)?f (v) ≥ 1 whenever u and v are at distance two apart. The span of f is the difference between the largest and the smallest numbers in f V (G). The λd-number for G, denoted by λ(G), is the minimum span over all L(d,1)-labelings of G. In this paper, a constructive labeling algorithm for the L(d,1)-labeling of Cartesian product of two complete graphs is presented. Based on this algorithm, the λd-numbers of some Cartesian product of two complete graphs are determined for 1 ≤ d ≤ 9.Copyright © 2014 American Scientific Publishers Copyright © 2014 American Scientific Publishers. Source


Hu D.-K.,Sichuan University | Hu D.-K.,Institutions of Higher Education of Sichuan Province | Lin J.,University of Electronic Science and Technology of China
Applied Mechanics and Materials | Year: 2013

A multi-feature bio-inspired model for scene image classification (MFBIM) is presented in this work; it extends the hierarchical feedforward model of the visual cortex. Firstly, each of three paths of classification uses each image property (i.e. shape, edge or color based features) independently. Then, BPNN assigns the category of an image based on the previous outputs. Experiments show that the model boosts the classification accuracy over the shape based model. Meanwhile, the proposed approach achieves a high accuracy comparable to other reported methods on publicly available color image dataset. © (2013) Trans Tech Publications, Switzerland. Source


Li Z.,Peking University | Shao Z.,Institutions of Higher Education of Sichuan Province | Shao Z.,Sichuan University | Zhu E.,Peking University | Xu J.,Peking University
Information Processing Letters | Year: 2015

A local k-coloring of a graph G is a function f:V(G)→{1,2,·,k} such that for each S⊆V(G), 2≤|S|≤3, there exist u,v ∈ S with |f(u)-f(v)| at least the size of the subgraph induced by S. The local chromatic number of G is χl(G)=min{k:G has a local k-coloring}. Chartrand et al. [2] asked: does there exist a graph Gk such that χl(Gk)=χ(Gk)=k? Furthermore, they conjectured that for every positive integer k, there exists a graph Gk with χl(G)=k such that every local k-coloring of Gk uses all of the colors 1,2,·,k. In this paper we give a affirmative answer to the problem and confirm the conjecture. © 2014 Published by Elsevier B.V. Source


Klavzar S.,University of Ljubljana | Klavzar S.,University of Maribor | Klavzar S.,Institute of Mathematics | Shao Z.,Institutions of Higher Education of Sichuan Province | Shao Z.,Sichuan University
International Journal of Computer Mathematics | Year: 2015

A local colouring of a graph G is a function c: V(G)→ℕ such that for each S ⊆ V(G), 2≤|S|≤3, there exist u, v∈S with |c(u)−c(v)| at least the number of edges in the subgraph induced by S. The maximum colour assigned by c is the value χℓ(c) of c, and the local chromatic number of G is χℓ(G)=min {χℓ(c): c is a local colouring of G}. In this note the local chromatic number is determined for Cartesian products G □ H, where G and GH are 3-colourable graphs. This result in part corrects an error from Omoomi and Pourmiri [On the local colourings of graphs, Ars Combin. 86 (2008), pp. 147–159]. It is also proved that if G and H are graphs such that χ(G)≤⌊ χℓ(H)/2 ⌋, then χℓ(G □ H)≤χℓ(H)+1. © 2014 Taylor & Francis. Source

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