Factor-Critical Property in 3-Dominating-Critical Graphs

A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$. A graph $G$ is said to be $\gamma$- vertex-critical if $\gamma(G-v)< \gamma(G)$, for every vertex $v$ in $G$. Let $G$ be a 2-connected $K_{1,5}$-free 3-vertex-critical graph. For any vertex $v \in V(G)$, we show that $G-v$ has a perfect matching (except two graphs), which is a conjecture posed by Ananchuen and Plummer.Comment: 8 page

On Murty-Simon Conjecture II

A graph is diameter two edge-critical if its diameter is two and the deletion of any edge increases the diameter. Murty and Simon conjectured that the number of edges in a diameter two edge-critical graph on $n$ vertices is at most $\lfloor \frac{n^{2}}{4} \rfloor$ and the extremal graph is the complete bipartite graph $K_{\lfloor \frac{n}{2} \rfloor, \lceil \frac{n}{2} \rceil}$. In the series papers [7-9], the Murty-Simon Conjecture stated by Haynes et al. is not the original conjecture, indeed, it is only for the diameter two edge-critical graphs of even order. In this paper, we completely prove the Murty-Simon Conjecture for the graphs whose complements have vertex connectivity $\ell$, where $\ell = 1, 2, 3$; and for the graphs whose complements have an independent vertex cut of cardinality at least three.Comment: 9 pages, submitted for publication on May 10, 201

A numerical procedure for recovering true scattering coefficients from measurements with wide-beam antennas

A numerical procedure for estimating the true scattering coefficient, sigma(sup 0), from measurements made using wide-beam antennas. The use of wide-beam antennas results in an inaccurate estimate of sigma(sup 0) if the narrow-beam approximation is used in the retrieval process for sigma(sup 0). To reduce this error, a correction procedure was proposed that estimates the error resulting from the narrow-beam approximation and uses the error to obtain a more accurate estimate of sigma(sup 0). An exponential model was assumed to take into account the variation of sigma(sup 0) with incidence angles, and the model parameters are estimated from measured data. Based on the model and knowledge of the antenna pattern, the procedure calculates the error due to the narrow-beam approximation. The procedure is shown to provide a significant improvement in estimation of sigma(sup 0) obtained with wide-beam antennas. The proposed procedure is also shown insensitive to the assumed sigma(sup 0) model

Algorithm and Architecture for Path Metric Aided Bit-Flipping Decoding of Polar Codes

Polar codes attract more and more attention of researchers in recent years, since its capacity achieving property. However, their error-correction performance under successive cancellation (SC) decoding is inferior to other modern channel codes at short or moderate blocklengths. SC-Flip (SCF) decoding algorithm shows higher performance than SC decoding by identifying possibly erroneous decisions made in initial SC decoding and flipping them in the sequential decoding attempts. However, it performs not well when there are more than one erroneous decisions in a codeword. In this paper, we propose a path metric aided bit-flipping decoding algorithm to identify and correct more errors efficiently. In this algorithm, the bit-flipping list is generated based on both log likelihood ratio (LLR) based path metric and bit-flipping metric. The path metric is used to verify the effectiveness of bit-flipping. In order to reduce the decoding latency and computational complexity, its corresponding pipeline architecture is designed. By applying these decoding algorithms and pipeline architecture, an improvement on error-correction performance can be got up to 0.25dB compared with SCF decoding at the frame error rate of $10^{-4}$, with low average decoding latency.Comment: 6 pages, 6 figures, IEEE Wireless Communications and Networking Conference (2019 WCNC

On the Existence of General Factors in Regular Graphs

Let $G$ be a graph, and $H\colon V(G)\to 2^\mathbb{N}$ a set function associated with $G$. A spanning subgraph $F$ of $G$ is called an $H$-factor if the degree of any vertex $v$ in $F$ belongs to the set $H(v)$. This paper contains two results on the existence of $H$-factors in regular graphs. First, we construct an $r$-regular graph without some given $H^*$-factor. In particular, this gives a negative answer to a problem recently posed by Akbari and Kano. Second, by using Lov\'asz's characterization theorem on the existence of $(g, f)$-factors, we find a sharp condition for the existence of general $H$-factors in $\{r, r+1\}$-graphs, in terms of the maximum and minimum of $H$. The result reduces to Thomassen's theorem for the case that $H(v)$ consists of the same two consecutive integers for all vertices $v$, and to Tutte's theorem if the graph is regular in addition.Comment: 10 page

μ-Oxalato-κ4 O 1,O 2:O 1′,O 2′-bis­[diaqua­(2,2′-bipyridyl-κ2 N,N′)zinc] bis­[2-(1H-benzotriazol-1-yl)acetate] hexa­hydrate

The asymmetric unit of the title compound, [Zn2(C2O4)(C10H8N2)2(H2O)4](C8H6N3O2)2·6H2O, contains one half of the centrosymmetric binuclear cation, one anion and three water mol­ecules. In the cation, the oxalate ligand bridges two ZnII ions in a bis-bidentate fashion, so each ZnII ion is coordinated by two O atoms from the oxalate ligand, two N atoms from two 2,2′-bipyridine ligands and two water mol­ecules in a distorted octa­hedral arrangement. The mean planes of the oxalate and 2,2′-bipyridine ligands form a dihedral angle of 80.0 (1)°. An extensive three-dimensional hydrogen-bonding network formed by classical O—H⋯O and O—H⋯N inter­actions consolidates the crystal packing