let l := u3(11). in this article, we classify groups with the same order and degree pattern as an almost simple group related to l. in fact, we prove that l, l:2 and l:3 are od-characterizable, and l:s3 is 5-fold od-characterizable.

1. Introduction. Let p be a prime number such that q — l{p — l) is also a prime. Let Q, be the set of symbols 1, • • • , p, and ® be a non-solvable transitive permutation group on 12. Such permutation groups were first considered by Galois in 1832 [I, §327; III, §262]: if the linear fractional group LF 2 (l) over the field of I elements, where I is a prime number not smaller than five, contains...

2 The Linearity of Expectation and small tweakings 11 2.1 Revisiting the Ramsey Number R(n, n) . . . . . . . . . . . . . . . . . . . 11 2.2 List Chromatic Number and minimum degree . . . . . . . . . . . . . . . 11 2.3 The Daykin-Erdős conjecture . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 An Example from Combinatorial Geometry . . . . . . . . . . . . . . . . . 14 2.5 Graphs with High...

Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation r, being random in other aspects and preserving the degree sequence. This can be done through Monte Carlo optimization procedures. Meanwhile, when tuning r, other n...

5 Degree distribution 10 5.1 Covariate description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2 Calibration of power-law distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Minization Küllback-Leibler divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Hill estimator of...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...