Let Fk denote the k-fan consisting of k triangles which intersect in exactly one common vertex, and Sn,k complete split graph order n a clique on vertices an independent set remaining each vertex is adjacent to set. In this paper, it shown that unique attaining maximum signless Laplacian spectral radius among all graphs containing no Fk, provided k?2 n?3k2?k?2.

During the last decade several research groups have published results on sufficient conditions for hamiltonicity of graphs in terms their spectral radius and signless Laplacian radius. Here we extend some these results. All our involve characterization exceptional graphs, i.e., all nonhamiltonian that satisfy condition. The proofs main are based Bondy–Chvátal closure, a degree sequence conditio...

let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...