JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 151-160.doi: 10.6040/j.issn.1671-9352.0.2022.316
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1 |
VALIANT L G . The complexity of computing the permanent[J]. Theoretical Computer Science, 1979, 8 (2): 189- 201.
doi: 10.1016/0304-3975(79)90044-6 |
2 |
MERRIS R , REBMAN K R , WATKINS W . Permanental polynomials of graphs[J]. Linear Algebra and Its Applications, 1981, 38, 273- 288.
doi: 10.1016/0024-3795(81)90026-4 |
3 |
BAPAT R B . A bound for the permanent of the Laplacian matrix[J]. Linear Algebra and Its Applications, 1986, 74, 219- 223.
doi: 10.1016/0024-3795(86)90124-2 |
4 | CASH G , GUTMAN I . The lapacian permanental polynomial: formulas and algorithms[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2004, 51 (51): 129- 136. |
5 |
GENG X Y , HU X , LI S C . Further results on permanental bounds for the Laplacian matrix of trees[J]. Linear and Multilinear Algebra, 2010, 58 (5): 571- 587.
doi: 10.1080/03081080902765583 |
6 |
GENG X Y , HU S N , LI S C . Permanental bounds of the Laplacian matrix of trees with given domination number[J]. Graphs and Combinatorics, 2015, 31 (5): 1423- 1436.
doi: 10.1007/s00373-014-1451-z |
7 | LI S C , LI Y , ZHANG X X . Edge-grafting theorems on permanents of Laplacian matrices of graphs and their applications[J]. The Electronic Journal of Linear Algebra, 2013, 26, 28- 48. |
8 |
LIU S Y . On the (signless) Laplacian permanental polynomials of graphs[J]. Graphs and Combinatorics, 2019, 35 (3): 787- 803.
doi: 10.1007/s00373-019-02033-2 |
9 | LIU X G , WU T Z . Computing the permanental polynomials of graphs[J]. Applied Mathematics and Computation, 2017, 304 (C): 103- 113. |
10 |
MERRIS R . The Laplacian permanental polynomial for trees[J]. Czechoslovak Mathematical Journal, 1982, 32 (3): 397- 403.
doi: 10.21136/CMJ.1982.101816 |
11 |
VRBA A . Principal subpermanents of the Laplacian matrix[J]. Linear and Multilinear Algebra, 1986, 19 (4): 335- 346.
doi: 10.1080/03081088608817728 |
12 | GOLDWASSER J L . Permanent of the Laplacian matrix of trees with a given matching[J]. Discrete Mathematics, 1986, 61 (2/3): 197- 212. |
13 |
BOTTI P , MERRIS R , VEGA C . Laplacian permanents of trees[J]. SIAM Journal on Discrete Mathematics, 1992, 5 (4): 460- 466.
doi: 10.1137/0405036 |
14 | LIU X G , WU T Z . Graphs determined by the (signless) Laplacian permanental polynomial[J]. Linear and Multilinear Algebra, 2017, 3599- 3615. |
15 |
FARIA I . Permanental roots and the star degree of a graph[J]. Linear Algebra and Its Applications, 1985, 64, 255- 265.
doi: 10.1016/0024-3795(85)90281-2 |
16 |
FARIA I . Multiplicity of integer roots of polynomials of graphs[J]. Linear Algebra and Its Applications, 1995, 229, 15- 35.
doi: 10.1016/0024-3795(93)00337-Y |
17 |
LI S C , ZHANG L . Permanental bounds for the signless Laplacian matrix of bipartite graphs and unicyclic graphs[J]. Linear and Multilinear Algebra, 2011, 59 (2): 145- 158.
doi: 10.1080/03081080903261467 |
18 |
LI S C , ZHANG L . Permanental bounds for the signless Laplacian matrix of a unicyclic graph with diameter d[J]. Graphs and Combinatorics, 2012, 28 (4): 531- 546.
doi: 10.1007/s00373-011-1057-7 |
19 |
WU T Z , ZHOU T , LV H Z . Further results on the star degree of graphs[J]. Applied Mathematics and Computation, 2022, 425, 127076.
doi: 10.1016/j.amc.2022.127076 |
20 |
BRUALDI R A , GOLDWASSER J L . Permanent of the Laplacian matrix of trees and bipartite graphs[J]. Discrete Mathematics, 1984, 48 (1): 1- 21.
doi: 10.1016/0012-365X(84)90127-4 |
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