The Signless Laplacian Spectral Radius of Unicyclic Graphs with Graph Constraints
نویسندگان
چکیده
In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.
منابع مشابه
The Signless Laplacian Estrada Index of Unicyclic Graphs
For a simple graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$, where $q^{}_1, q^{}_2, dots, q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...
متن کاملOn the Signless Laplacian Spectral Radius of Unicyclic Graphs with Fixed Matching Number
We determine the graph with the largest signless Laplacian spectral radius among all unicyclic graphs with fixed matching number.
متن کاملThe Signless Dirichlet Spectral Radius of Unicyclic Graphs
Let G be a simple connected graph with pendant vertex set ∂V and nonpendant vertex set V0. The signless Laplacian matrix of G is denoted by Q(G). The signless Dirichlet eigenvalue is a real number λ such that there exists a function f ̸= 0 on V (G) such that Q(G)f(u) = λf(u) for u ∈ V0 and f(u) = 0 for u ∈ ∂V . The signless Dirichlet spectral radius λ(G) is the largest signless Dirichlet eigenva...
متن کاملThe Signless Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with a Given Girth
Let U(n, g) and B(n, g) be the set of unicyclic graphs and bicyclic graphs on n vertices with girth g, respectively. Let B1(n, g) be the subclass of B(n, g) consisting of all bicyclic graphs with two edge-disjoint cycles and B2(n, g) = B(n, g)\B1(n, g). This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in U(n, g) and B(n, g), respectivel...
متن کاملSIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$ and $A(G)$ the adjacency matrix of $G$. The signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...
متن کامل