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Let $f(n)$ be the maximum number of edges in a graph on $n$ vertices in which no two cycles have the same length. P. Erdos raised the problem of determining $f(n)$ (see J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, New York, 1976), p.247, Problem 11). We present the problems, conjectures related to this problems and we summarize the know results. We make the following conjecture: \par \noindent{\bf Conjecture } $$\lim\sb {n \to \infty} {f(n)-n \over \sqrt n} = \sqrt {2 + \frac{4}{9}}.$$

The rank of tensors is not additive with respect to the direct sum.

The CD inequalities are introduced to imply the gradient estimate of Laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,1) and CD(K,n).

The set of all non-increasing nonnegative integers sequence $\pi=$ ($d(v_1 ),$ $d(v_2 ),$ $...,$ $d(v_n )$) is denoted by $NS_n$. A sequence $\pi\in NS_n$ is said to be graphic if it is the degree sequence of a simple graph $G$ on $n$ vertices, and such a graph $G$ is called a realization of $\pi$. The set of all graphic sequences in $NS_n$ is denoted by $GS_n$. A graphical sequence $\pi$ is potentially $H$-graphical if there is a realization of $\pi$ containing $H$ as a subgraph, while $\pi$ is forcibly $H$-graphical if every realization of $\pi$ contains $H$ as a subgraph. Let $K_k$ denote a complete graph on $k$ vertices. Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). This paper summarizes briefly some recent results on potentially $K_{m}-G$-graphic sequences and give a useful classification for determining $\sigma(H,n)$.