Related papers: L-Borderenergetic graphs and Normalized Laplacian …

In this paper, we compute normalized Laplacian spectra of central graph of a regular graph, central vertex join and central edge join of two regular graphs. Also, we determine their Kemeny's constant and degree Kirchhoff index.

In this paper, we determine the maximal Laplacian and signless Laplacian spectral radii for graphs with fixed number of vertices and domination number, and characterize the extremal graphs respectively.

The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and…

Let $\mathcal{H}$ be a connected $k$-uniform hypergraph on $n$ vertices and $m$ hyperedges. In [A.~Banerjee, On the spectrum of hypergraph, Linear Algebra and its Application, 614(2021), 82--110], Anirban Banerjee introduced a new adjacency…

In this paper we compute common neighbourhood (abbreviated as CN) spectrum and energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a consequence of our results we show that the commuting conjugacy…

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…

Given a graph $A$ on a group $G$ and an equivalence relation $B$ on $G$, the $B$ super$A$ graph, whose vertex set is $G$ and two vertices $g$, $h$ are adjacent if and only if there exist $g^{\prime} \in[g]$ and $h^{\prime} \in[h]$ such that…

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…

We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…

Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…

The graph entropy describes the structural information of graph. Motivated by the definition of graph entropy in general graphs, the graph entropy of hypergraphs based on Laplacian degree are defined. Some results on graph entropy of simple…

This paper presents a comprehensive theoretical analysis of the graph p-Laplacian regularized framelet network (pL-UFG) to establish a solid understanding of its properties. We conduct a convergence analysis on pL-UFG, addressing the gap in…

We address the Laplacian on a perturbed periodic graph which might not be a periodic graph. We present a class of perturbed graphs for which the essential spectra of the Laplacians are stable even when the graphs are perturbed by adding and…

In this paper, we define the non-commuting graph associated to a Lie algebra L and obtain some basic graph properties such as connectivity, diameter, girth, Hamiltonian and Eulerian. Moreover, planarity, outer planarity and isomorphism…

We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of…

Let $R$ be a Hermitian matrix. The energy of $R$, $\mathcal{E}(R)$, corresponds to the sum of the absolute values of its eigenvalues. In this work it is obtained two lower bounds for $\mathcal{E}(R).$ The first one generalizes a lower bound…

Let $f(D(i, j), d_i, d_j)$ be a real function symmetric in $i$ and $j$ with the property that $f(d, (1+o(1))np, (1+o(1))np)=(1+o(1))f(d, np, np)$ for $d=1,2$. Let $G$ be a graph, $d_i$ denote the degree of a vertex $i$ of $G$ and $D(i, j)$…

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…

A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral…

According to a recent conjecture, isospectral objects have different nodal count sequences. We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counter-examples to this conjecture. In…