# Habibeh Panahbar's research while affiliated with Persian Gulf University and other places

## Publications (4)

Article
Full-text available
The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G , which in turn is equal to the sum of the singular values of the adjacency matrix of G. Let X, Y and Z be matrices, such that X+Y= Z. The Ky Fan theorem establishes an inequality between the sum of the singular values of Z and the sum of the sum of the singu...
Article
Full-text available
Let $G$ be a graph with a vertex weight $\omega$ and the vertices $v_1,\ldots,v_n$. The Laplacian matrix of $G$ with respect to $\omega$ is defined as $L_\omega(G)=\mathrm{diag}(\omega(v_1),\cdots,\omega(v_n))-A(G)$, where $A(G)$ is the adjacency matrix of $G$. Let $\mu_1,\cdots,\mu_n$ be eigenvalues of $L_\omega(G)$. Then the Laplacian energy of $... Article Full-text available The energy of a graph$G$is equal to the sum of the absolute values of the eigenvalues of$G$, which in turn is equal to the sum of the singular values of the adjacency matrix of$G$. Let$X$,$Y$and$Z$be matrices, such that$X+Y= Z$. The Ky Fan theorem establishes an inequality between the sum of the singular values of$Z\$ and the sum of the...

## Citations

... If G is k-transmission regular, then T r(G) = kI n , where I n denotes the identity matrix of order n. In [21,22], a transmission version of Laplacian matrix of a connected graph G, was defined as ...
... Then the matrices L deg (G) = D deg (G) − A(G) and L † deg (G) = A(G) + D deg (G) are called Laplacian and signless Laplacian matrix of G, respectively (see [8], [9], [19], [20], [21] and [22]). These matrices was generalized for arbitrary vertex weighted graphs (see [26] and [27]). Let G be a simple graph with the vertex weight ω. ...
... In this present study inspired by the work in [7], we investigate the laplacian energy of fuzzy graph's eccentricity version denoted by LE ε G , we define the laplacian eccentricity matrix as ...
... Then the matrices L deg (G) = D deg (G) − A(G) and L † deg (G) = A(G) + D deg (G) are called Laplacian and signless Laplacian matrix of G, respectively (see [8], [9], [19], [20], [21] and [22]). These matrices was generalized for arbitrary vertex weighted graphs (see [26] and [27]). Let G be a simple graph with the vertex weight ω. ...