Results 1 to 10 of about 1,493,991 (168)

On the permanental polynomial and permanental sum of signed graphs [PDF]

Discrete Mathematics Letters, 2022
Let Ġ = (G, σ) be a signed graph, where G is its underlying graph and σ is its sign function (defined on the edge set E(G) of G). Let A(Ġ) be the adjacency matrix of Ġ.
Zikai Tang, Qiyue Li, Hanyuan Deng
doaj   +4 more sources

The extremal pentagon-chain polymers with respect to permanental sum. [PDF]

Sci Rep, 2020
The permanental sum of a graph G can be defined as the sum of absolute value of coefficients of permanental polynomial of G. It is closely related to stability of structure of a graph, and its computing complexity is #P-complete.
Wu T, Wang H, Zhang S, Deng K.
europepmc   +5 more sources

The Extremal Permanental Sum for a Quasi-Tree Graph [PDF]

Complexity, 2019
Let G be a graph and A(G) the adjacency matrix of G. The permanent of matrix (xI-A(G)) is called the permanental polynomial of G. The permanental sum of G is the sum of the absolute values of the coefficients of permanental polynomial of G. Computing the
Tingzeng Wu, Huazhong Lü
doaj   +4 more sources

Solution to a Conjecture on the Permanental Sum

Axioms
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 (I+A(G)) is called the permanental sum of G.
Tingzeng Wu, Xueji Jiu
doaj   +3 more sources

Extremal Bicyclic Graphs with Respect to Permanental Sums and Hosoya Indices

Axioms
Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs.
Tingzeng Wu, Yinggang Bai, Shoujun Xu
doaj   +3 more sources

The Graphs Whose Permanental Polynomials Are Symmetric

Discussiones Mathematicae Graph Theory, 2018
The permanental polynomial π(G,x)=∑i=0nbixn−i$\pi (G,x) = \sum\nolimits_{i = 0}^n {b_i x^{n - i} }$ of a graph G is symmetric if bi = bn−i for each i. In this paper, we characterize the graphs with symmetric permanental polynomials.
Li Wei
doaj   +2 more sources

Determinantal Processes and Independence [PDF]

, 2006
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).
Hough, J. Ben, Krishnapur, Manjunath, Peres, Yuval, Virág, Bálint   +3 more
core   +3 more sources

Permanental fields, loop soups and continuous additive functionals [PDF]

, 2015
A permanental field, $\psi=\{\psi(\nu),\nu\in {\mathcal{V}}\}$, is a particular stochastic process indexed by a space of measures on a set $S$. It is determined by a kernel $u(x,y)$, $x,y\in S$, that need not be symmetric and is allowed to be infinite on
Jan, Yves Le, Marcus, Michael B., Rosen, Jay   +2 more
core   +2 more sources

Algorithms for Two Types of Topological Indices

Algorithms
Topological indices are closely related to the stability and physical properties (such as the boiling point) of chemical molecules. The permanental sum and Hosoya index are two topological indices that are strongly associated with molecular structure. In
Fengqin Deng, Tingzeng Wu
doaj   +2 more sources

A study on determination of some graphs by Laplacian and signless Laplacian permanental polynomials

AKCE International Journal of Graphs and Combinatorics, 2023
The permanent of an n × n matrix [Formula: see text] is defined as [Formula: see text] where the sum is taken over all permutations σ of [Formula: see text] The permanental polynomial of M, denoted by [Formula: see text] is [Formula: see text] where In ...
Aqib Khan, Pratima Panigrahi, Swarup Kumar Panda   +2 more
doaj   +1 more source