Bounds on the largest eigenvalues of trees with a given size of matching

AbstractVery little is known about upper bound for the largest eigenvalue of a tree with a given size of matching. In this paper, we find some upper bounds for the largest eigenvalue of a tree in terms of the number of vertices and the size of matchings, which improve some known results

Square nearly nonpositive sign pattern matrices

AbstractA sign pattern matrix A is called square nearly nonpositive if all entries but one of A2 are nonpositive. We characterize the irreducible sign pattern matrices that are square nearly nonpositive. Further we determine the maximum (resp. minimum) number of negative entries that can occur in A2 when A is irreducible square nearly nonpositive (SNNP), and then we characterize the sign patterns that achieve this maximum (resp. minimum) number. Finally, we discuss some spectral properties of the sign patterns which are square nonpositive or square nearly nonpositive

Digraphs with degree equivalent induced subdigraphs

AbstractA digraph G of order n is said to have property Dk if every induced subdigraph of order n − k in G has the same degree sequence. In this paper, we characterize all digraphs with property Dk when k = 1, 2

On potentially nilpotent double star sign patterns

summary:A matrix \Cal A whose entries come from the set $\{+,-,0\}$ is called a {\it sign pattern matrix}, or {\it sign pattern}. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by ${\cal DSSP}(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in ${\cal DSSP}(3,2)$ and ${\cal DSSP}(5,2)$, and prove that one sign pattern in ${\cal DSSP}(3,2)$ is potentially stable