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Start Over Coverage 1039-1048

1. Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs

Creator:
Das, Kinkar Ch and Liu, Muhuo
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
mathematics, spectral radius, (signless) Laplacian spectral radius, clique number, 13, and 51
Language:
English
Description:
n this paper, the upper and lower bounds for the quotient of spectral radius (Laplacian spectral radius, signless Laplacian spectral radius) and the clique number together with the corresponding extremal graphs in the class of connected graphs with n vertices and clique number ω(2 ≤ ω ≤ n) are determined. As a consequence of our results, two conjectures given in Aouchiche (2006) and Hansen (2010) are proved., Kinkar Ch. Das, Muhuo Liu., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Subgroups of odd depth—a necessary condition

Creator:
Burciu, Sebastian
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
depth of group algebras, finite group, and faithful representation
Language:
English
Description:
This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with $\{0,1\}$-entries to have maximal rank. The entries of the matrix correspond to the sizes of the intersections of the subgroup with any of its conjugate.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public