arXiv subjects

Chunxiang Wang

Publications and source records attributed to Chunxiang Wang.

45 records · Page 3Linked to original sources

arXiv2018

Do satellite galaxies trace matter in galaxy clusters?

The spatial distribution of satellite galaxies encodes rich information of the structure and assembly history of galaxy clusters. In this paper, we select a redMaPPer cluster sample in SDSS Stripe 82 region with $0.1 \le z \le 0.33$, $20<λ<100$ and $P_{\rm cen}>0.7$. Using the high-quality weak lensing data from CS82 Survey, we constrain the mass profile of this sample. Then we compare directly the mass density profile with the satellite number density profile. We find that the total mass and number density profiles have the same shape, both well fitted by an NFW profile. The scale radii agree with each other within 1$σ$ error ($r_{\rm s,gal}=0.34_{-0.03}^{+0.04}$Mpc vs $r_{\rm s}=0.37_{-0.10}^{+0.15}$Mpc ).

astro-ph.CO↗

arXiv2017

Joint Calibration of Panoramic Camera and Lidar Based on Supervised Learning

In view of contemporary panoramic camera-laser scanner system, the traditional calibration method is not suitable for panoramic cameras whose imaging model is extremely nonlinear. The method based on statistical optimization has the disadvantage that the requirement of the number of laser scanner's channels is relatively high. Calibration equipments with extreme accuracy for panoramic camera-laser scanner system are costly. Facing all these in the calibration of panoramic camera-laser scanner system, a method based on supervised learning is proposed. Firstly, corresponding feature points of panoramic images and point clouds are gained to generate the training dataset by designing a round calibration object. Furthermore, the traditional calibration problem is transformed into a multiple nonlinear regression optimization problem by designing a supervised learning network with preprocessing of the panoramic imaging model. Back propagation algorithm is utilized to regress the rotation and translation matrix with high accuracy. Experimental results show that this method can quickly regress the calibration parameters and the accuracy is better than the traditional calibration method and the method based on statistical optimization. The calibration accuracy of this method is really high, and it is more highly-automated.

cs.CV↗

arXiv2017

On the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges

For a molecular graph, the first multiplicative Zagreb index $Π_1$ is equal to the product of the square of the degree of the vertices, while the second multiplicative Zagreb index $Π_2$ is equal to the product of the endvertex degree of each edge over all edges. Denote by $\mathbb{G}_{n,k}$ the set of graphs with $n$ vertices and $k$ cut edges. In this paper, we explore graphs in terms of a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges are provided. Furthermore, we characterize graphs with the largest and smallest $Π_1(G)$ and $Π_2(G)$ in $\mathbb{G}_{n,k}$, and our results extend and enrich some known conclusions.

math.CO↗

arXiv2017

Sharp upper bounds for multiplicative Zagreb indices of bipartite graphs with given diameter

The first multiplicative Zagreb index of a graph $G$ is the product of the square of every vertex degree, while the second multiplicative Zagreb index is the product of the degree of each edge over all edges. In our work, we explore the multiplicative Zagreb indices of bipartite graphs of order $n$ with diameter $d$, and sharp upper bounds are obtained for these indices of graphs in $\mathcal{B}(n,d)$, where $\mathcal{B}(n, d)$ is the set of all $n$-vertex bipartite graphs with the diameter $d$. In addition, we explore the relationship between the maximal multiplicative Zagreb indices of graphs \textcolor{blue}{within} $\mathcal{B}(n, d)$. As consequences, those bipartite graphs with the largest, second-largest and smallest multiplicative Zagreb indices are characterized, and our results extend and enrich some known conclusions.

math.CO↗

arXiv2017

On extremal multiplicative Zagreb indices of trees with given number of vertices of maximum degree

The first multiplicative Zagreb index of a graph $G$ is the product of the square of every vertex degree, while the second multiplicative Zagreb index is the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore the trees in terms of given number of vertices of maximum degree. The maximum and minimum values of $\prod_1(G) $ and $\prod_2(G) $ of trees with arbitrary number of maximum degree are provided. In addition, the corresponding extremal graphs are characterized.

math.CO↗

arXiv2016

On extremal multiplicative Zagreb indices of trees with given domination number

For a graph $G$, the first multiplicative Zagreb index $\prod_1$ is equal to the product of squares of the vertex degrees, and the second multiplicative Zagreb index $\prod_2$ is equal to the product of the products of degrees of pairs of adjacent vertices. The (mutiplicative) Zagreb indices have been the focus of considerable research in computational chemistry dating back to Gutman and Trinajstić in 1972. In this paper, we explore the mutiplicative Zagreb indices in terms of arbitrary domination number. The sharp upper and lower bounds of $\prod_1(G)$ and $\prod_2(G)$ are given. In addition, the corresponding extreme graphs are charaterized.

math.CO↗

arXiv2016

Total domination polynomials of graphs

Given a graph $G$, a total dominating set $D_t$ is a vertex set that every vertex of $G$ is adjacent to some vertices of $D_t$ and let $d_t(G,i)$ be the number of all total dominating sets with size $i$. The total domination polynomial, defined as $D_t(G,x)=\sum\limits_{i=1}^{| V(G)|} d_t(G,i)x^i$, recently has been one of the considerable extended research in the field of domination theory. In this paper, we obtain the vertex-reduction and edge-reduction formulas of total domination polynomials. As consequences, we give the total domination polynomials for paths and cycles. Additionally, we determine the sharp upper bounds of total domination polynomials for trees and characterize the corresponding graphs attaining such bounds. Finally, we use the reduction-formulas to investigate the relations between vertex sets and total domination polynomials in $G$.

math.CO↗

arXiv2016

Further results on degree based topological indices of certain chemical networks

There are various topological indices such as degree based topological indices, distance based topological indices and counting related topological indices etc. These topological indices correlate certain physicochemical properties such as boiling point, stability of chemical compounds. In this paper, we compute the sum-connectivity index and multiplicative Zagreb indices for certain networks of chemical importance like silicate networks, hexagonal networks, oxide networks, and honeycomb networks. Moreover, a comparative study using computer-based graphs has been made to clarify their nature for these families of networks.

math.CO↗

arXiv2016

Cacti with Extremal PI Index

The vertex PI index $PI(G) = \sum_{xy \in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947. A connected graph is a cactus if any two of its cycles have at most one common vertex. In this paper, we completely determine the extremal graphs with the largest and smallest vertex PI indices among all the cacti. As a consequence, we obtain the sharp bounds with corresponding extremal cacti and extend a known result.

math.CO↗