Related papers: On spectral radius of strongly connected digraphs

Identifying graphs with extremal properties is an extensively studied topic in spectral graph theory. In this paper, we study the log-concavity of a type of iteration sequence related to the $\alpha$-normal weighted incidence matrices which…

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. A minimizer graph is such that minimizes the spectral radius among all connected graphs on $n$ vertices with diameter $d$. The minimizer graphs are known for…

A graph is minimally $k$-connected ($k$-edge-connected) if it is $k$-connected ($k$-edge-connected) and deleting arbitrary chosen edge always leaves a graph which is not $k$-connected ($k$-edge-connected). A classic result of minimally…

A dissociation set of a graph is a set of vertices which induces a subgraph with maximum degree less than or equal to one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we study the…

Let $\mathcal{G}_{n, \beta^*}$ $(\mathcal{G}^*_{n,\beta^*})$ be the set of all (connected) graphs of order $n$ with fractional matching number $\beta^*$. In this paper, the graphs with maximal spectral radius in $\mathcal{G}_{n,\beta^*}$…

A connected and acyclic hypergraph is called a supertree. In this paper we mainly focus on the spectral radii of uniform supertrees. Li, Shao and Qi determined the first two $k$-uniform supertrees with large spectral radii among all the…

Let $\mathcal{B}(n,q)$ be the class of block graphs on $n$ vertices having all their blocks of the same size. We prove that if $G\in \mathcal{B}(n,q)$ has at most three pairwise adjacent cut vertices then the minimum spectral radius…

In this paper, we determine the graphs which have the minimal spectral radius among all the connected graphs of order $n$ and the independence number $\lceil\frac{n}{2}\rceil-1.$

Let $\mathcal{D}_{n,\tau}$ be the set of all simple connected graphs of order $n$ and dissociation number $\tau.$ In this paper, we study the minimum size and the minimum spectral radius of graphs in $\mathcal{D}_{n,\tau}$ in connection…

A graph is trivial if it contains one vertex and no edges. The essential connectivity $\kappa^{\prime}$ of $G$ is defined to be the minimum number of vertices of $G$ whose removal produces a disconnected graph with at least two non-trivial…

A digraph is strongly connected if it has a directed path from $x$ to $y$ for every ordered pair of distinct vertices $x, y$ and it is strongly $k$-connected if it has at least $k+1$ vertices and remains strongly connected when we delete…

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known…

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ($n,g$ being fixed), which graph minimizes the Laplacian spectral radius? We prove that the graph…

The spectral radius of a graph is the largest modulus of an eigenvalue of its adjacency matrix. Let $\mathcal{C}_{n, e}$ be the set of all the connected simple graphs with $n$ vertices and $n - 1 + e$ edges. Here, we solve the spectral…

Let $G$ be a connected nonregular graphs of order $n$ with maximum degree $\Delta$ that attains the maximum spectral radius. Liu and Li (2008) proposed a conjecture stating that $G$ has a degree sequence $(\Delta,\ldots,\Delta,\delta)$ with…

It is known that the spectral radius of a digraph with k edges is \le \sqrt{k}, and that this inequality is strict except when k is a perfect square. For k=m^2 + \ell, \ell fixed, m large, Friedland showed that the optimal digraph is…

Let $\mu(G)$ denote the spectral radius of a graph $G$. We partly confirm a conjecture due to Nikiforov, which is a spectral radius analogue of the well-known Erd\H{o}s-S\'os Conjecture that any tree of order $t$ is contained in a graph of…

The spectral radius of a uniform hypergraph $G$ is the the maximum modulus of the eigenvalues of the adjacency tensor of $G$. For $k\ge 2$, among connected $k$-uniform hypergraphs with $m\ge 1$ edges, we show that the $k$-uniform loose path…

For a graph $G$, the spectral radius of $G$ is the largest eigenvalue of its adjacency matrix. A connected factor of $G$ is a connected spanning subgraph of $G$. For example, a spanning tree of $G$ is a 1-connected factor of $G$. Let $G$ be…

We prove that there exist four operations such that given any two strongly $2$-connected digraphs $H$ and $D$ where $H$ is a butterfly-minor of $D$, there exists a sequence $D_0,\dots, D_n$ where $D_0=H$, $D_n=D$ and for every $0\leq i\leq…