Bounds on the index of the Signless Laplacian of a graph involving the average degree of neighbors of a vertex

A shock absorber apparatus connected in series relationship respective to the polished rod and bridle of a pumpjack unit. The shock absorber includes a housing within which there is supported a plurality of resilient packer members stacked in sandwiched relationship. The packer members have an axial passageway formed therethrough, with the passageway of each packer member being aligned with one another, so that the polished rod is telescopingly received therethrough. The bottom of the housing is supported by the bridle, while the polished rod is supported by a plate member which bears against the uppermost packer member. This places all of the resilient packer members in compression, with the force of the compression being proportional to the weight of the sucker rod.

[1]  Curtis Greene.  Some Partitions Associated with a Partially Ordered Set , 1976, J. Comb. Theory, Ser. A.

[2]  Rajeev Motwani,et al.  Algorithms for Multi-product Pricing , 2004, ICALP.

[3]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[4]  V. Sunder,et al.  The Laplacian spectrum of a graph , 1990 .

[5]  Bang Ye Wu,et al.  Polynomial time algorithms for some minimum latency problems , 2000, Inf. Process. Lett..

[6]  ChenYan.  PROPERTIES OF SPECTRA OF GRAPHS AND LINE GRAPHS , 2002 .

[7]  Maria-Florina Balcan,et al.  Approximation algorithms and online mechanisms for item pricing , 2006, EC '06.

[8]  T. D. Morley,et al.  Eigenvalues of the Laplacian of a graph , 1985 .

[9]  R. Merris.  A note on Laplacian graph eigenvalues , 1998 .

[10]  Michael Doob,et al.  Spectra of graphs , 1980 .

[11]  Pierre Hansen,et al.  Automated conjectures on upper bounds for the largest Laplacian eigenvalue of graphs , 2005 .

[12]  Kinkar Ch. Das,et al.  A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs , 2004 .

[13]  Oscar Rojo,et al.  An always nontrivial upper bound for Laplacian graph eigenvalues , 2000 .

[14]  Bang Ye Wu,et al.  Exact algorithms for the minimum latency problem , 2004, Inf. Process. Lett..

[15]  Vladlen Koltun,et al.  Near-Optimal Pricing in Near-Linear Time , 2005, WADS.

[16]  B. Roy.  Nombre chromatique et plus longs chemins d'un graphe , 1967 .

[17]  Xu Huai-juan.  A New Upper Bound for the Laplacian Spectral Radius of Graphs , 2007 .

[18]  Qi Jian.  The Spectral Radius of Laplacian Matrices and Quasi-Laplacian Matrices of Graphs , 2003 .

[19]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[20]  Venkatesan Guruswami,et al.  On profit-maximizing envy-free pricing , 2005, SODA '05.

[21]  D. Cvetkovic,et al.  Signless Laplacians of finite graphs , 2007 .

[22]  Xiao-Dong Zhang,et al.  On the Laplacian eigenvalues of a graph , 1998 .

[23]  Nathan Linial.  Extending the Greene-Kleitman Theorem to Directed Graphs , 1981, J. Comb. Theory, Ser. A.

[24]  Xiao-Dong Zhang,et al.  Two sharp upper bounds for the Laplacian eigenvalues , 2004 .

[25]  Xiao-Dong Zhang,et al.  The Laplacian eigenvalues of mixed graphs , 2003 .

[26]  Irith Ben-Arroyo Hartman,et al.  Berge's conjecture on directed path partitions - a survey , 2006, Discret. Math..

[27]  Daniel J. Kleitman,et al.  The Structure of Sperner k-Families , 1976, J. Comb. Theory, Ser. A.

[28]  Yong-Liang Pan,et al.  de Caen's inequality and bounds on the largest Laplacian eigenvalue of a graph , 2001 .

[29]  Kinkar Ch. Das,et al.  An improved upper bound for Laplacian graph eigenvalues , 2003 .

[30]  Piotr Krysta,et al.  Single-minded unlimited supply pricing on sparse instances , 2006, SODA '06.

[31]  D. Cvetkovic.  Signless Laplacians and line graphs , 2005 .

[32]  Alfredo García Olaverri,et al.  A note on the traveling repairman problem , 2002, Networks.

[33]  Erik D. Demaine,et al.  Combination can be hard: approximability of the unique coverage problem , 2006, SODA '06.

[34]  Abraham Berman,et al.  Lower bounds for the eigenvalues of Laplacian matrices , 2000 .