The kK_{r+1}-free n-vertex graph with maximum t-clique spectral radius is K_{k-1} joined to T_r(n-k+1) for sufficiently large n.
On some properties of nonnegative weakly irreducible tensors
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abstract
In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the definition of stochastic tensors. Then we show that every nonnegative weakly irreducible tensor with spectral radius being one is diagonally similar to a unique weakly irreducible stochastic tensor. Based on it, we prove some important lemmas, which help us to generalize the results related. Some counterexamples are provided to show that some conclusions for nonnegative irreducible tensors do not hold for nonnegative weakly irreducible tensors.
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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