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

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## Publications (4)

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...

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 $...

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. ...