Examining A Renormalizable Supersymmetric SO(10) Model

We examine a renormalizable SUSY SO(10) model without fine-tuning. We show how to construct MSSM doublets and to predict proton decay. We find that in the minimal set of Yukawa couplings the model is consistent with the experiments, while including $120_H$ to fit the data there are inconsistencies.Comment: 18 page

List (d,1)-total labelling of graphs embedded in surfaces

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we consider the list version of (d,1)-total labelling of graphs. Let G be a graph embedded in a surface with Euler characteristic $\epsilon$ whose maximum degree $\Delta(G)$ is sufficiently large. We prove that the (d,1)-total choosability $C_{d,1}^T(G)$ of $G$ is at most $\Delta(G)+2d$.Comment: 6 page

Modelling the Self-similarity in Complex Networks Based on Coulomb's Law

Recently, self-similarity of complex networks have attracted much attention. Fractal dimension of complex network is an open issue. Hub repulsion plays an important role in fractal topologies. This paper models the repulsion among the nodes in the complex networks in calculation of the fractal dimension of the networks. The Coulomb's law is adopted to represent the repulse between two nodes of the network quantitatively. A new method to calculate the fractal dimension of complex networks is proposed. The Sierpinski triangle network and some real complex networks are investigated. The results are illustrated to show that the new model of self-similarity of complex networks is reasonable and efficient.Comment: 25 pages, 11 figure