Results 51 to 60 of about 550 (132)
Riemannian-geometric entropy for measuring network complexity [PDF]
, 2016 A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry.
Felice, Domenico +3 more
core +2 more sources
Mathematische Nachrichten, Volume 297, Issue 5, Page 1749-1771, May 2024.Abstract Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schrödinger operators on domains. We review some known results obtained in the last 10 years, unify several approaches used to achieve such bounds, and extend their scope to a large class of linear and nonlinear operators. We also use landscape functions to
Delio Mugnolo
wiley +1 more source
Bounds for Incidence Energy of Some Graphs
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 Let G be a simple graph. The incidence energy (IE for short) of G is defined as the sum of the singular values of the incidence matrix. In this paper, a new upper bound for IE of graphs in terms of the maximum degree is given. Meanwhile, bounds for IE of the line graph of a semiregular graph and the paraline graph of a regular graph are obtained.
Weizhong Wang, Dong Yang, Magdy A. Ezzat
wiley +1 more source
Randi\'c energy and Randi\'c eigenvalues [PDF]
, 2014 Let $G$ be a graph of order $n$, and $d_i$ the degree of a vertex $v_i$ of $G$. The Randi\'c matrix ${\bf R}=(r_{ij})$ of $G$ is defined by $r_{ij} = 1 / \sqrt{d_jd_j}$ if the vertices $v_i$ and $v_j$ are adjacent in $G$ and $r_{ij}=0$ otherwise.
Li, Xueliang, Wang, Jianfeng
core
Laplacian spectral characterization of some double starlike trees [PDF]
, 2013 A tree is called double starlike if it has exactly two vertices of degree greater than two. Let $H(p,n,q)$ denote the double starlike tree obtained by attaching $p$ pendant vertices to one pendant vertex of the path $P_n$ and $q$ pendant vertices to the ...
Liu, Xiaogang, Lu, Pengli
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Distance Spectra of Some Double Join Operations of Graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In literature, several types of join operations of two graphs based on subdivision graph, Q‐graph, R‐graph, and total graph have been introduced, and their spectral properties have been studied. In this paper, we introduce a new double join operation based on (H1, H2)‐merged subdivision graph.
B. J. Manjunatha +4 more
wiley +1 more source
Energy, Laplacian energy of double graphs and new families of equienergetic graphs [PDF]
, 2013 For a graph $G$ with vertex set $V(G)=\{v_1, v_2, \cdots, v_n\}$, the extended double cover $G^*$ is a bipartite graph with bipartition (X, Y), $X=\{x_1, x_2, \cdots, x_n\}$ and $Y=\{y_1, y_2, \cdots, y_n\}$, where two vertices $x_i$ and $y_j$ are ...
A Ganie, Hilal, S. Pirzada
core
On the diameter and incidence energy of iterated total graphs
, 2018 The total graph of $G$, $\mathcal T(G)$ is the graph whose set of vertices is the union of the sets of vertices and edges of $G$, where two vertices are adjacent if and only if they stand for either incident or adjacent elements in $G$.
Lenes, Eber +3 more
core +1 more source
On the Signless Laplacian ABC-Spectral Properties of a Graph
MathematicsIn the paper, we introduce the signless Laplacian ABC-matrix Q̃(G)=D¯(G)+Ã(G), where D¯(G) is the diagonal matrix of ABC-degrees and Ã(G) is the ABC-matrix of G. The eigenvalues of the matrix Q̃(G) are the signless Laplacian ABC-eigenvalues of G.
Bilal A. Rather +2 more
doaj +1 more source
Laplacian coefficients of unicyclic graphs with the number of leaves and girth
, 2013 Let $G$ be a graph of order $n$ and let $\mathcal{L}(G,\lambda)=\sum_{k=0}^n (-1)^{k}c_{k}(G)\lambda^{n-k}$ be the characteristic polynomial of its Laplacian matrix. Motivated by Ili\'{c} and Ili\'{c}'s conjecture [A. Ili\'{c}, M.
Zhang, Jie, Zhang, Xiao-Dong
core +1 more source