Let G be a simple undirected graph. The permanental sum of G is equal to the permanent of
the matrix I+ A (G), where I is the identity matrix and A (G) is an adjacency matrix of G. The …

Let G be any simple undirected graph and let Q (G) be the signless Laplacian matrix of G.
The polynomial ϕ (Q (G), x)= per (x I− Q (G)) is called the signless Laplacian permanental …

Let G be a graph with n vertices and m edges. A (G) and I denote, respectively, the
adjacency matrix of G and an n by n identity matrix. For a graph G, the permanent of matrix …

Let A (G) be an adjacency matrix of a graph G. Then the polynomial π (G, x)= per (x I− A (G))
is called the permanental polynomial of G, and the permanental sum of G is the sum of the …

An expression of the coefficient of immanantal polynomial of an n× n matrix is present.
Moreover, we give expressions of the coefficient of immanantal polynomials of combinatorial …

Structural properties of graphs and networks have been investigated across scientific
disciplines ranging from mathematics to structural chemistry. Structural branching, cyclicity …

Let A (G) be the adjacency matrix of a graph G. The permanental polynomial of G is defined
as π (G, x)= per (xI-A (G)) π (G, x)= per (x IA (G)). The permanental sum of G can be defined …

Let G be a simple undirected graph, I the identity matrix, and A (G) an adjacency matrix of G.
Then the permanental sum of G equals to the permanent of the matrix I+ A (G) I+ A (G). Since …

In 1983, Borowiecki and J\'o\'zwiak posed an open problem of characterizing graphs with
purely imaginary per-spectrum. The most general result, although a partial solution, was …

The permanent of a square matrix\(M=(m_ {ij}) _ {k\times k}\) is\(per (M)=\sum _\sigma\prod _
{i= 1}^{k} m_ {i\sigma (i)}\), where the sum is taken over all permutations\(\sigma\) of the …