Abstract We present two new sufficient conditions in terms of the spectral radius $$\rho (G)$$ ρ ( G ) guaranteeing that a k -connected graph G is Hamilton-connected, unless belongs to collection exceptional graphs. use Bondy–Chvátal cl...

we give further results for perron-frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. we indicate two techniques for establishing the main theorem ofperron and frobenius on the numerical range. in the rst method, we use acorresponding version of wielandt's lemma. the second technique involves graphtheory.

The p-spectral radius of a uniform hypergraph G of order n is de…ned for every real number p 1 as (p) (G) = max jx1j + + jxnj = 1 r! X fi1;:::;irg2E(G) xi1 xir : It generalizes several hypergraph parameters, including the Lagrangian, the spectral radius, and the number of edges. The paper presents solutions to several extremal problems about the p-spectral radius of k-partite and k-chromatic hy...

In 1962, Erdős gave a sufficient condition for Hamilton cycles in terms of the vertex number, edge number, and minimum degree of graphs which generalized Ore’s theorem. One year later, Moon and Moser gave an analogous result for Hamilton cycles in balanced bipartite graphs. In this paper we present the spectral analogues of Erdős’ theorem and Moon-Moser’s theorem, respectively. Let Gk n be the ...

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the ext...