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The odd wheel $W_{2k+1}$ is the graph formed by joining a vertex to a cycle of length $2k$. In this paper, we investigate the largest value of the spectral radius of the adjacency matrix of an $n$-vertex graph that does not contain $W_{2k+1}$. We determine the structure of the spectral extremal graphs for all $kgeq 2, k otin {4,5}$. When $k=2$, we show that these spectral extremal graphs are among the Tur{a}n-extremal graphs on $n$ vertices that do not contain $W_{2k+1}$ and have the maximum number of edges, but when $kgeq 9$, we show that the family of spectral extremal graphs and the family of Tur{a}n-extremal graphs are disjoint.
Let $tgeq3$ and $G$ be a graph of order $n,$ with no $K_{2,t}$ minor. If $n>400t^{6}$, then the spectral radius $muleft( Gright) $ satisfies [ muleft( Gright) leqfrac{t-1}{2}+sqrt{n+frac{t^{2}-2t-3}{4}}, ] with equality if and only if $nequiv1$ $(ope
Let $F_{a_1,dots,a_k}$ be a graph consisting of $k$ cycles of odd length $2a_1+1,dots, 2a_k+1$, respectively which intersect in exactly a common vertex, where $kgeq1$ and $a_1ge a_2ge cdotsge a_kge 1$. In this paper, we present a sharp upper bound fo
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
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 classify the connected non-bipartite integral graphs with spectral radius three.