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In this paper, we show that an order $m$ dimension 2 tensor is primitive if and only if its majorization matrix is primitive, and then we obtain the characterization of order $m$ dimension 2 strongly primitive tensors and the bound of the strongly primitive degree. Furthermore, we study the properties of strongly primitive tensors with $ngeq 3$, and propose some problems for further research.
In this paper, we characterize the extremal digraphs with the maximal or minimal $alpha$-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size $m$. These digraph classes are
In 1965, Motzkin and Straus [5] provided a new proof of Turans theorem based on a continuous characterization of the clique number of a graph using the Lagrangian of a graph. This new proof aroused interests in the study of Lagrangians of r-uniform g
Given a proper edge coloring $varphi$ of a graph $G$, we define the palette $S_{G}(v,varphi)$ of a vertex $v in V(G)$ as the set of all colors appearing on edges incident with $v$. The palette index $check s(G)$ of $G$ is the minimum number of distin
Visibility representation of digraphs was introduced by Axenovich, Beveridge, Hutch-inson, and West (emph{SIAM J. Discrete Math.} {bf 27}(3) (2013) 1429--1449) as a natural generalization of $t$-bar visibility representation of undirected graphs. A {
A {it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpa