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Relationship between heart girth, serum progesterone and superovulation response ofdonor Holstein cows

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Asian pacific Journal of Reproduction 2019年第3期8卷 118-123页

作者： Abdel-Tawab AYKhalil Ahmed Abdel-Wahab Rabie LAbdel Aziz Department of Theriogenology Faculty of Veterinary MedicineBeni-Suef UniversityBeni-SuefEgypt Physiology Department Faculty of Veterinary MedicineMinia UniversityEl-MiniaEgypt

Objective: To determine effects of variations of heart girth, volume trait on embryo quality grade, and to explore the relationship between heart girth and circulating progesterone and correlations of circulating progesterone with embryo quality grade in superstimulated donor Holstein cows. Methods: Nineteen cows were subjected to a standard superstimulation protocol using follicle stimulating hormone. Blood samples were collected before superovulation, at insemination and at collection of embryos for progesterone analysis. Embryo quality grades were compared between high and low heart girth donors. Moreover, Pearson's correlations were determined between heart girth, progesterone and embryo quality. Results: Variation of heart girth was not associated with significant differences in embryo quality grade between high and low heart girth donor cows (P>0.05). However, we observed a significantly higher percentage of the third-grade embryo (24.09%) in low heart girth donors compared to 9.64% in high heart girth donors. Moreover, the percentage of the transferable embryo was numerically higher and that of the degenerated embryo was numerically lower in low heart girth cows. Donor cows with low response to superovulation (total structures ≤ 3) expressed numerically higher mean heart girth, compared to donors with high (total structures>15) and medium (total structures = 4-15) superovulation. Heart girth and body weight of donor cows were moderately correlated (r=0.45, Pgirth may influence the response of Holstein cows to superovulation;however, future studies with a higher number of cows are warranted to clarify significant inf

关键词： Heart girth Superovulation Embryo quality Progesterone Holstein cow

On the girth of Tanner (5,7) Quasi-Cyclic LDPC Codes

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Journal of Harbin Institute of Technology(New Series) 2017年第6期24卷 80-89页

作者： Hengzhou Xu Baoming Bai Dan Feng Cheng Sun State Key Laboratory of Integrated Services Networks Xidian UniversityXi’an 710071China

The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.

关键词： LDPC codes quasi-cyclic Tanner graph girth

Results on diameter-stable graphs related to girth

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Journal of Shanghai University(English Edition) 2010年第3期14卷 167-169页

作者：许承德顾瑞 Department of Mathematics College of SciencesShanghai University

A graph G is said to be an （l,d）-graph （with respect to edges） if d（G-E）≤d,E E（G） such that ｜ E ｜≤l-1.The l-diameter-stable graphs are （l,d）-graphs with diameter d.In this paper some new results on d... 详细信息

关键词： diameter-stable graph line-persistence girth isomorphic short（x y）-path

Fractional Coloring Planar Graphs under Steinberg-type Conditions

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Acta Mathematica Sinica,English Series 2023年第5期39卷 904-922页

作者： Xiao Lan HU Jia Ao LI School of Mathematics and Statistics&Hubei Key Laboratory of Mathematical Sciences Central China Normal UniversityWuhan 430079P.R.China School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071P.R.China

A Steinberg-type conjecture on circular coloring is recently proposed that for any prime p≥5,every planar graph of girth p without cycles of length from p+1 to p(p-2)is Cp-colorable(that is,it admits a homomorphism to the odd cycle Cp).The assumption of p≥5 being prime number is necessary,and this conjecture implies a special case of Jaeger’s Conjecture that every planar graph of girth 2p-2 is Cp-colorable for prime p≥5.In this paper,combining our previous results,we show the fractional coloring version of this conjecture is true.Particularly,the p=5 case of our fractional coloring result shows that every planar graph of girth 5 without cycles of length from 6 to 15 admits a homomorphism to the Petersen graph.

关键词： Fractional coloring circular coloring planar graphs girth homomorphism

The Signless Laplacian Spectral Radius of Tricyclic Graphs with a Given girth

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Journal of Mathematical Research with Applications 2014年第4期34卷 379-391页

作者： Lu QIAO Ligong WANG Department of Applied Mathematics School of ScienceNorthwestern Polytechnical University

A tricyclic graph G =(V(G), E(G)) is a connected and simple graph such that|E(G)| = |V(G)|+2. Let Tg nbe the set of all tricyclic graphs on n vertices with girth g. In this paper, we will show that there exists the unique graph which has the largest signless Laplacian spectral radius among all tricyclic graphs with girth g containing exactly three(resp., four)cycles. And at the same time, we also give an upper bound of the signless Laplacian spectral radius and the extremal graph having the largest signless Laplacian spectral radius in Tg n,where g is even.

关键词： tricyclic graph signless Laplacian spectral radius girth

On Jumped Wenger Graphs

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Communications in Mathematical Research 2022年第2期38卷 319-332页

作者： Li-Ping Wang Daqing Wan Weiqiong Wang Haiyan Zhou State Key Laboratory of Information Security Institute of Information EngineeringCASChina School of Cyber Security University of Chinese Academy of SciencesChina Department of Mathematics University of CaliforniaIrvineCAUSA School of Science Chan’an UniversityXi'anChina School of Mathematics Nanjing Normal UniversityNanjingChina

We introduce a new infinite class of bipartite graphs, called jumped Wenger graphs, which has a similar structure with Wenger graphs. We give a tight upper bound of the diameter for these graphs and the exact diameter... 详细信息

关键词： Wenger graphs diameter girth algebraic graph theory

Edge Coloring of Graphs with Applications in Coding Theory

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China Communications 2021年第1期18卷 181-195页

作者： Ghaffar Raeisi Mohammad Gholami Department of Mathematical Sciences Shahrekord UniversityShahrekordP.O.Box 115Iran

In this paper,a new type of edge coloring of graphs together with an algorithm for such an edge coloring is presented to construct some columnweight three low-density parity-check(LDPC)codes whose Tanner graphs are free of 4-cycles.This kind of edge coloring is applied on some well-known classes of graphs such as complete graphs and complete bipartite graphs to generate some column-weight 3 LDPC codes having flexibility in terms of code length and rate.Interestingly,the constructed(3;k)-regular codes with regularities k=4;5;:::;22 have lengths n=12;20;26,35;48;57;70;88;104;117;140;155;176;204;228;247;280;301;330;having minimum block length compared to the best known similar codes in the literature.In addition to linear complexity of generating such parity-check matrices,they can be considered as the base matrices of some quasi-cyclic(QC)LDPC codes with maximum achievable girth 18,which inherit the low-complexity encoder implementations of QC-LDPC codes.Simulation results show that the QC-LDPC codes with large girth lifted from the constructed base matrices have good performances and outperform random codes,progressive edge growth LDPC codes,some finite fields and group rings based QC-LDPC codes and also have a close competition to the standard IEEE 802.16e(WiMAX)code.

关键词： low-density parity-check code edge coloring Quasi-cyclic LDPC code girth AWGN channel

Backbone Coloring for Triangle-free Planar Graphs

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 819-824页

作者： Yue-hua BU Shui-ming ZHANG Xingzhi College Zhejiang Normal UniversityJinhua 321004China

Let G be a graph and H a subgraph of G. A backbone-k-coloring of （G, H） is a mapping f： V（G） → {1,2,…,k} such that If（u）- f（v）｜ ≥ 2 if uv ∈ E（H） and ｜f（u）- f（v）｜ ≥ 1 if uv ∈ E（G）／E（H）. T... 详细信息

Let G be a graph and H a subgraph of G. A backbone-k-coloring of （G, H） is a mapping f： V（G） → {1,2,…,k} such that If（u）- f（v）｜ ≥ 2 if uv ∈ E（H） and ｜f（u）- f（v）｜ ≥ 1 if uv ∈ E（G）／E（H）. The backbone chromatic number of （G, H） denoted by Xb（G, H） is the smallest integer k such that （G, H） has a backbone-k-coloring. In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad（G）〈 3, then there exists a spanning tree T of G such that Xb（G, T） ≤ 4.

关键词： backbone coloring spanning tree girth maximum average degree

New Improvements on Connectivity of Cages

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1163-1172页

作者： Hong Liang LU Yun Jian WU Qing Lin YU Yu Qing LIN Department of Mathematics Xi'an Jiaotong University Xi'an 710049 P. R. China Department of Mathematics Southeast University Nanjing 211189 P. R. China Department of Mathematics and Statistics Thompson Rivers University Kamloops V2C 5N3 BC Canada School of Electrical Engineering and Computer Science The University of Newcastle Newcastle NSW 2308 Australia

A （δ, g）-cage is a δ-regular graph with girth g and with the least possible number of vertices. In this paper, we show that all （δ, g）-cages with odd girth g ≥ 9 are r-connected, where （r - 1）2 ≤δ ＋ x/δ - 2 〈 r2 and all （δ, g）-cages with even girth g 〉 10 are r-connected, where r is the largest integer satisfying r（r-1）2/4 ＋ 1 ＋ 2r（r - 1） ≤δ. These results support a conjecture of Fkl, Huang and Rodger that all （δ, g）-cages are 6-connected.

关键词： Cage girth superconnectivity