相关论文: Spectral radius and clique partitions of graphs
In this paper, we determine the graphs whose spectral radius and distance spectral radius attain maximum and minimum among all complements of clique trees. Furthermore, we also determine the graphs whose spectral radius and distance…
We give a bound on the spectral radius of subgraphs of regular graphs with given order and diameter. We give a lower bound on the smallest eigenvalue of a nonbipartite regular graph of given order and diameter.
This paper presents a sharp upper bound for the spectral radius of simple digraphs with described number of arcs. Further, the extremal graphs which attain the maximum spectral radius among all simple digraphs with fixed arcs are…
In this paper, we obtain two spectral upper bounds for the $k$-independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than $k$. We construct graphs that attain equality for our first…
This paper generalizes and unifies the existing spectral bounds on the $k$-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than $k$. The previous bounds known in the literature…
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…
In this paper we obtain some upper bounds for $b$-chromatic number of $K_{1,t}$ -free graphs, graphs with given minimum clique partition and bipartite graphs. These bounds are in terms of either clique number or chromatic number of graphs…
Let $k_r(n,\delta)$ be the minimum number of $r$-cliques in graphs with $n$ vertices and minimum degree $\delta$. We evaluate $k_r(n,\delta)$ for $\delta \leq 4n/5$ and some other cases. Moreover, we give a construction, which we conjecture…
We present a number of relations involving the number of cliques in a graph and its spectral radius.
In this paper, we present a sharp upper and lower bounds for the signless Laplacian spectral radius of graphs in terms of clique number. Moreover, the extremal graphs which attain the upper and lower bounds are characterized. In addition,…
The spectral radius of a graph is the spectral radius of its adjacency matrix. A threshold graph is a simple graph whose vertices can be ordered as $v_1, v_2, \ldots, v_n$, so that for each $2 \le i \le n$, vertex $v_i$ is either adjacent…
The spectral radius and rank of a graph are defined to be the spectral radius and rank of its adjacency matrix, respectively. It is an important problem in spectral extremal graph theory to determine the extremal graph that has the maximum…
Recently Chase determined the maximum possible number of cliques of size $t$ in a graph on $n$ vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
We study the size of the shadow of $k$-uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a function of the degree bound and $k$. We show that cliques are…
Let $G(n,k)$ be the class of clique trees on $n$ vertices and zero forcing number $k$, where $\left \lfloor \frac{n}{2} \right \rfloor + 1 \le k \le n-1$ and each block is a clique of size at least $3$. In this article, we proved the…
The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This…
In this paper, we present two sharp upper bounds for the spectral radius of (bipartite) graphs with forbidden a star forest and characterize all extremal graphs. Moreover, the minimum least eigenvalue of the adjacency matrix of graph with…
We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.
Let $\lambda^{*}$ be the maximum spectral radius of connected irregular graphs on $n$ vertices with maximum degree $\Delta$. Liu, Shen and Wang (2007) conjectured that $\lim_{n\rightarrow…