Results 1 to 10 of about 479 (182)
On the permanental polynomial and permanental sum of signed graphs [PDF]
Discrete Mathematics Letters, 2022 Summary: Let \(\dot{G}= (G, \sigma)\) be a signed graph, where \(G\) is its underlying graph and \(\sigma\) is its sign function (defined on the edge set \(E(G)\) of \(G\)). Let \(A(\dot{G})\) be the adjacency matrix of \(\dot{G}\). The polynomial \(\pi(\dot{G}, x) = \operatorname{per}(xI - A (\dot{G}))\) is called the permanental polynomial of \(\dot ...
Zikai Tang, Qiyue Li, Hanyuan Deng
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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
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The Characterizing Properties of (Signless) Laplacian Permanental Polynomials of Almost Complete Graphs [PDF]
Journal of Mathematics, 2021 Let G be a graph with n vertices, and let LG and QG denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic ...
Tingzeng Wu, Tian Zhou
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Computing the permanental polynomial of 4k-intercyclic bipartite graphs
The American Journal of CombinatoricsLet \(G\) be a bipartite graph with adjacency matrix \(A(G)\). The characteristic polynomial \(\phi(G,x)=\det(xI-A(G))\) and the permanental polynomial \(\pi(G,x) = \operatorname{per}(xI-A(G))\) are both graph invariants used to distinguish graphs.
Ravindra Bapat +2 more
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The properties of the Laplacian permanental polynomials of graphs
AIMS MathematicsIn this paper, some properties of the Laplacian permanental polynomials of graphs are given. First, we provide a formula to evaluate the coefficients of the Laplacian permanental polynomial.
Wei Li
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Computing the permanental polynomial of a matrix from a combinatorial viewpoint [PDF]
, 2011 Recently, in the book [A Combinatorial Approach to Matrix Theory and Its Applications, CRC Press (2009)] the authors proposed a combinatorial approach to matrix theory by means of graph theory.
BELARDO, Francesco +2 more
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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 +2 more
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Generalized Permanental Polynomials of Graphs [PDF]
Symmetry, 2019 The search for complete graph invariants is an important problem in graph theory and computer science. Two networks with a different structure can be distinguished from each other by complete graph invariants. In order to find a complete graph invariant, we introduce the generalized permanental polynomials of graphs.
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Permanental vectors with nonsymmetric kernels [PDF]
, 2017 A permanental vector with a symmetric kernel and index $2$ is a squared Gaussian vector. The definition of permanental vectors is a natural extension of the definition of squared Gaussian vectors to nonsymmetric kernels and to positive indexes.
Eisenbaum, Nathalie
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Permanental polynomials of graphs
Linear Algebra and its Applications, 1981 AbstractThe first section surveys recent results on the permanental polynomial of a square matrix A, i.e., per(xI – A). The second section concerns the permanental polynomial of the adjacency matrix of a graph. The final section is an introduction to the permanental polynomial of the Laplacian matrix of a graph.
Merris, Russell +2 more
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