Related papers: On the Estrada index of unicyclic and bicyclic sig…

The Estrada index of a graph $G$ is defined as $EE(G)=\sum_{i=1}^ne^{\lambda_i}$, where $\lambda_1,$ $ \lambda_2,\ldots, \lambda_n$ are the eigenvalues of the adjacency matrix of $G$. In this paper, we characterize the unique bipartite…

Let $G$ be a simple graph of order $n$, let $\lambda_1(G),\lambda_2(G),...,\lambda_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{\lambda_i(G)}$. In this paper we…

Let $\Gamma=(K_n,H)$ be a signed complete graph whose negative edges induce a subgraph $H$. Let $A(\Gamma)$ be the adjacency matrix of the signed graph $\Gamma$. The largest eigenvalue of $A(\Gamma)$ is called the index of $\Gamma$. In this…

Let $G$ be a graph on $n$ vertices and $\lambda_1,\lambda_2,\ldots,\lambda_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{\lambda_i}.$ In this work, using a different demonstration technique, new lower…

The index of a signed graph is the largest eigenvalue of its adjacency matrix. For positive integers $n$ and $m\le n^2/4$, we determine the maximal index of complete signed graphs with $n$ vertices and $m$ negative edges. This settles (the…

Let $G$ be a graph on $n$ vertices and $\lambda_1,\lambda_2,\ldots,\lambda_n$ its eigenvalues. The Estrada index of $G$ is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. In this paper, we present…

Let $\Gamma=(K_{n},H^-)$ be a signed complete graph whose negative edges induce a subgraph $H$. The index of $\Gamma$ is the largest eigenvalue of its adjacency matrix. In this paper we study the index of $\Gamma$ when $H$ is a unicyclic…

Various properties of a hypergraph can be explored through its spectrum. In this paper,we estimate the bound for the sum of $t,\,t\in[1,n]$, largest eigenvalues of a $k$-uniform hypergraph of order $n$. Also, we characterize the $k$-uniform…

In this paper, we focus on the index ( largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As applications, we determine the…

The D-eigenvalues {\mu}_1,{\mu}_2,...,{\mu}_{n} of a connected graph G are the eigenvalues of its distance matrix. The distance Estrada index of G is defined in [15] as DEE=DEE(G)=\Sigma_{i=1}^n e^{{\mu}_{i}} In this paper, we give better…

Let $x_1, x_2, \dots, x_n$ be the eigenvalues of a signed graph $\Gamma$ of order $n$. The energy of $\Gamma$ is defined as $E(\Gamma)=\sum^{n}_{j=1}|x_j|.$ Let $\mathcal{P}_n^4$ be obtained by connecting a vertex of the negative circle…

For a 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…

A signed graph is one that features two types of edges: positive and negative. Balanced signed graphs are those in which all cycles contain an even number of positive edges. In the adjacency matrix of a signed graph, entries can be $0$,…

Let $G$ be a graph on $n$ vertices and $\lambda_1\geq \lambda_2\geq \ldots \geq \lambda_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{\lambda_i}.$ In this work, we using an increasing sequence converging…

A signed graph $\Gamma$ is said to be determined by its spectrum if every signed graph with the same spectrum as $\Gamma$ is switching isomorphic with $\Gamma$. Here it is proved that the path $P_n$, interpreted as a signed graph, is…

A signed graph $\Gamma(G)$ is a graph with a sign attached to each of its edges, where $G$ is the underlying graph of $\Gamma(G)$. The energy of a signed graph $\Gamma(G)$ is the sum of the absolute values of the eigenvalues of the…

A signed graph is a pair $(G,\Sigma)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V=\{1,\ldots,n\}$ and $\Sigma\subseteq E$. The edges in $\Sigma$ are called odd and the other edges of $E$…

Let $\lambda_1,\lambda_2,\cdots,\lambda_n$ be the eigenvalues of the distance matrix of a connected graph $G$. The distance Estrada index of $G$ is defined as $DEE(G)=\sum_{i=1}^ne^{\lambda_i}$. In this note, we present new lower and upper…

Uniform hypergraphs have a natural one-to-one correspondence to tensors. In this paper, we investigate the Estrada index and subgraph centrality of an $m$-uniform hypergraph $\mathcal{H}$ via the adjacency tensor. We establish some bounds…

Let $G$ be a simple graph with $n$ vertices and let $\mu_1 \geqslant \mu_2 \geqslant...\geqslant \mu_{n - 1} \geqslant \mu_n = 0$ be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as $LEE (G)…