in this paper, it was shown that , where  and , and , where  is not prime and , are od-characterizable.

the prime graph $gamma(g)$ of a group $g$ is a graph with vertex set $pi(g)$, the set of primes dividing the order of $g$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $g$ of order $pq$. let $pi(g)={p_{1},p_{2},...,p_{k}}$. for $pinpi(g)$, set $deg(p):=|{q inpi(g)| psim q}|$, which is called the degree of $p$. we also set $d(g):...

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.

The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...

Many graphs arising in various information networks exhibit the “power law” behavior – the number of vertices of degree k is proportional to k−β for some positive β. We show that if β > 2.5, the largest eigenvalue of a random power law graph is almost surely (1+o(1)) √ m where m is the maximum degree. When 2 < β < 2.5, the largest eigenvalue is heavily concentrated at cm3−β for some constant c ...

In this paper, we address the problem of fuzzy rule-based pattern recognition with reject options. These options are made possible thanks to simple rules whose satisfaction level is expressed by the value of dedicated operators that aggregate degrees of typicality. Results obtained with the proposed classifier on articicial and real data are given.

Samples from stochastic signals with suucient complexity need reveal only a little unexpected agreement, in order to reject the hypothesis that they are independent. The mere failure of a test of statistical independence can thereby serve as a basis for recognizing patterns conndently, provided they possess enough degrees-of-freedom. This paper discusses exploitation of this statistical princip...