ﻻ يوجد ملخص باللغة العربية
Let $G$ denote a bipartite graph with $e$ edges without isolated vertices. It was known that the spectral radius of $G$ is at most the square root of $e$, and the upper bound is attained if and only if $G$ is a complete bipartite graph. Suppose that $G$ is not a complete bipartite graph, and $e-1$ and $e+1$ are not twin primes. We determine the maximal spectral radius of $G$. As a byproduct of our study, we obtain a spectral characterization of a pair $(e-1, e+1)$ of integers to be a pair of twin primes.
Let k, p, q be positive integers with k < p < q+1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph Kp,q of bipartition orders p and q by deleting k edges is attained when the deleting e
In this paper, we classify the connected non-bipartite integral graphs with spectral radius three.
Let $G$ be a simple graph with vertex set $V(G) = {v_1 ,v_2 ,cdots ,v_n}$. The Harary matrix $RD(G)$ of $G$, which is initially called the reciprocal distance matrix, is an $n times n$ matrix whose $(i,j)$-entry is equal to $frac{1}{d_{ij}}$ if $i ot
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 forbidden a
Write $rholeft( Gright) $ for the spectral radius of a graph $G$ and $S_{n,r}$ for the join $K_{r}veeoverline{K}_{n-r}.$ Let $n>rgeq2$ and $G$ be a $K_{r+1}$-saturated graph of order $n.$ Recently Kim, Kim, Kostochka, and O determined exactly the