Related papers: Energy of signed digraphs

Let $D$ be a simple digraph with eigenvalues $z_1,z_2,...,z_n$. The energy of $D$ is defined as $E(D)= \sum_{i=1}^n |Re(z_i)|$, is the real part of the eigenvalue $z_i$. In this paper a lower bound will be obtained for the spectral radius…

Answering some questions of Gutman, we show that, except for four specific trees, every connected graph G of order n, with no cycle of order 4 and with maximum degree at most 3, has energy greater that its order. Here, the energy of a graph…

We construct infinitely many signed graphs having symmetric spectrum, by using the NEPS and rooted product of signed graphs. We also present a method for constructing large cospectral signed graphs. Although the obtained family contains…

We study the energy per vertex in regular graphs. For every k, we give an upper bound for the energy per vertex of a k-regular graph, and show that a graph attains the upper bound if and only if it is the disjoint union of incidence graphs…

The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph, which is proposed first by Gutman and Wagner [The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177--2187].…

The energy of a graph was introduced by {\sc Gutman} in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized…

The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Let $s^+(G), s^-(G)$ denote the sum of the squares of the positive and negative eigenvalues of $G$, respectively. It was…

We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph $D_{r,s,\ell}$. Using switching equivalence, we reduce the spectrum to the real parts of the two cycle gains and obtain an…

The energy of a simple graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let $C_n$ denote the cycle of order $n$ and $P^{6,6}_n$ the graph obtained from joining two cycles…

A signed graph is a graph whose edges are given (-1,+1) weights. In such a graph, the sign of a cycle is the product of the signs of its edges. A signed graph is called balanced if its adjacency matrix is similar to the adjacency matrix of…

Harshitha et al. recently introduced Seidel energy of graphs with self loops. In this paper, we extend some of their results by giving a necessary and sufficient condition for the Seidel energy of a looped graph to be equal to the Seidel…

Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ be the roots of its matching…

The energy of a graph is the sum of the absolute values of its adjacency eigenvalues. For integral circulant graphs $\ICG(n,\mathcal{D})$ of order $n=p^2q^3$, where $p$ and $q$ are distinct odd primes, we prove that the adjacency…

In [Curtin and Pourgholi, A group sum inequality and its application to power graphs, J. Algebraic Combinatorics, 2014], it is proved that among all directed power graphs of groups of a given order $ n $, the directed power graph of cyclic…

Let $G$ be a graph with $n$ vertices and $m$ edges. The energy $E$ of the graph $G$ is defined as the sum of the moduli of the adjacency eigenvalues $\lambda_{1} \geq \lambda_{2} \geq \ldots \geq \lambda_{n}$ of $G$: $$…

The Laplacian energy of a digraph $G$ is defined as $\sum_{i=1}^n \lambda_i^2$, where $\lambda_i$ are the eigenvalues of the Laplacian matrix of $G$. A (di)graph $G$ is said to be $H$-free if it does not contain a copy of the fixed…

Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for \lambda \neq -1,0. For cographs with balanced cotrees we determine explicitly the highest value for…

The energy $E$ of a graph is defined to be the sum of the absolute values of its eigenvalues. Nikiforov in {\it ``V. Nikiforov, The energy of $C_4$-free graphs of bounded degree, Lin. Algebra Appl. 428(2008), 2569--2573"} proposed two…

Let $\G$ be an oriented graph of order $n$ and $\a_1,\a_2,..., \a_n$ denote all the eigenvalues of the skew-adjacency matrix of $\G.$ The skew energy $\displaystyle{\cal E}_s(\G)= \sum_{i=1}^{n} |\a_i|.$ In this paper, the oriented…

The energy of a vertex $v_i$ in a graph $G$ is defined as $\mathcal{E}_G(v_i) = |A|_{ii}$, where $A$ is the adjacency matrix of $G$, $A^*$ denotes the conjugate transpose of $A$, and $|A| = (AA^*)^{1/2}$. The total energy of the graph,…