Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)
156
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Let $S_{1}(m, d, k)$ be the $k$-uniform supertree obtained from a loose path $P:v_{1}, e_{1}, v_{2}, ldots,v_{d}, e_{d}, v_{d+1}$ with length $d$ by attaching $m-d$ edges at vertex $v_{lfloorfrac{d}{2}rfloor+1}.$ Let $mathbb{S}(m,d,k)$ be the set of $k$-uniform supertrees with $m$ edges and diameter $d$ and $q(G)$ be the signless Laplacian spectral radius of a $k$-uniform hypergraph $G$. In this paper, we mainly determine $S_{1}(m,d,k)$ with the largest signless Laplacian spectral radius among all supertrees in $mathbb{S}(m,d,k)$ for $3leq dleq m-1$. Furthermore, we determine the unique uniform supertree with the maximum signless Laplacian spectral radius among all the uniform supertrees with $n$ vertices and pendent edges (vertices).
rate research
Read More
Tur{a}n type extremal problem is how to maximize the number of edges over all graphs which do not contain fixed forbidden subgraphs. Similarly, spectral Tur{a}n type extremal problem is how to maximize (signless Laplacian) spectral radius over all graphs which do not contain fixed subgraphs. In this paper, we first present a stability result for $kcdot P_3$ in terms of the number of edges and then determine all extremal graphs maximizing the signless Laplacian spectral radius over all graphs which do not contain a fixed linear forest with at most two odd paths or $kcdot P_3$ as a subgraph, respectively.
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 for the signless Laplacian spectral radius of all $F_{a_1,dots,a_k}$-free graphs and characterize all extremal graphs which attain the bound. The stability methods and structure of graphs associated with the eigenvalue are adapted for the proof.
A connected graph $G$ is a cactus if any two of its cycles have at most one common vertex. Let $ell_n^m$ be the set of cacti on $n$ vertices with matching number $m.$ S.C. Li and M.J. Zhang determined the unique graph with the maximum signless Laplacian spectral radius among all cacti in $ell_n^m$ with $n=2m$. In this paper, we characterize the case $ngeq 2m+1$. This confirms the conjecture of Li and Zhang(S.C. Li, M.J. Zhang, On the signless Laplacian index of cacti with a given number of pendant vetices, Linear Algebra Appl. 436, 2012, 4400--4411). Further, we characterize the unique graph with the maximum signless Laplacian spectral radius among all cacti on $n$ vertices.
In this paper, we present a spectral sufficient condition for a graph to be Hamilton-connected in terms of signless Laplacian spectral radius with large minimum degree.
In this paper, we give some bounds for principal eigenvector and spectral radius of connected uniform hypergraphs in terms of vertex degrees, the diameter, and the number of vertices and edges.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
