Results 51 to 60 of about 110,880 (163)
On a conjecture for the signless Laplacian eigenvalues
Linear Algebra and its Applications, 2014 Let $G$ be a simple graph with $n$ vertices and $e(G)$ edges, and $q_1(G)\geq q_2(G)\geq\cdots\geq q_n(G)\geq0$ be the signless Laplacian eigenvalues of $G.$ Let $S_k^+(G)=\sum_{i=1}^{k}q_i(G),$ where $k=1, 2, \ldots, n.$ F. Ashraf et al. conjectured that $S_k^+(G)\leq e(G)+\binom{k+1}{2}$ for $k=1, 2, \ldots, n.$ In this paper, we give various upper ...
Jieshan Yang, Lihua You
openaire +3 more sources
Spectra of Graphs Resulting from Various Graph Operations and Products: a Survey
Special Matrices, 2018 Let G be a graph on n vertices and A(G), L(G), and |L|(G) be the adjacency matrix, Laplacian matrix and signless Laplacian matrix of G, respectively. The paper is essentially a survey of known results about the spectra of the adjacency, Laplacian and ...
Barik S., Kalita D., Pati S., Sahoo G.
doaj +1 more source
Construction for the Sequences of Q‐Borderenergetic Graphs
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This research intends to construct a signless Laplacian spectrum of the complement of any k‐regular graph G with order n. Through application of the join of two arbitrary graphs, a new class of Q‐borderenergetic graphs is determined with proof. As indicated in the research, with a regular Q‐borderenergetic graph, sequences of regular Q‐borderenergetic ...
Bo Deng +4 more
wiley +1 more source
Spectral Results on Some Hamiltonian Properties of Graphs [PDF]
Romanian Journal of Mathematics and Computer Science, 2014 Using Lotker’s interlacing theorem on the Laplacian eigenvalues of a graph in [5] and Wang and Belardo’s interlacing theorem on the signless Laplacian eigenvalues of a graph in [6], we in this note obtain spectral conditions for some Hamiltonian ...
Rao Li
doaj
The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph
Linear Algebra and its Applications, 2015 In this paper, we show that the largest Laplacian H-eigenvalue of a $k$-uniform nontrivial hypergraph is strictly larger than the maximum degree when $k$ is even. A tight lower bound for this eigenvalue is given. For a connected even-uniform hypergraph, this lower bound is achieved if and only if it is a hyperstar.
Hu, Shenglong, Qi, Liqun, Xie, Jinshan
openaire +2 more sources
Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 In this paper, for a connected graph G and a real α≠0, we define a new graph invariant σα(G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G.
Ş. Burcu Bozkurt Altındağ
doaj +1 more source
A relation between the Laplacian and signless Laplacian eigenvalues of a graph [PDF]
Journal of Algebraic Combinatorics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akbari, S +3 more
openaire +2 more sources
On the distance and distance signless Laplacian eigenvalues of graphs and the smallest Gersgorin disc [PDF]
, 2018 The \emph{distance matrix} of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between the $i$th and $j$th vertices of $G$. The \emph{distance signless Laplacian matrix} of the graph $G$ is $D_Q(G)=D(G)+Tr(G)$, where $Tr(G)$
Panigrahi, Pratima, Atik, Fouzul
core +1 more source
Some improved bounds on two energy-like invariants of some derived graphs
Open Mathematics, 2019 Given a simple graph G, its Laplacian-energy-like invariant LEL(G) and incidence energy IE(G) are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. This paper obtains some improved bounds on LEL and
Cui Shu-Yu, Tian Gui-Xian
doaj +1 more source
Variation of sum of two largest eigenvalues of the distance matrices of four-leaf graph
Journal of Hebei University of Science and Technology, 2020 In order to accurately obtain the extremum of the distance eigenvalues of fowr-leaf graphs under tow graph transformations in any case, two graph transformations of four-leaf graphs and the results of the above problems were given by using the properties
Zhe LYU, Yubin GAO
doaj +1 more source