JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 87-92.doi: 10.6040/j.issn.1671-9352.0.2020.344

Previous Articles    

Inverse of Kronecker product of integrally invertible graphs

WANG Xia1, BIAN Hong1*, YU Hai-zheng2   

  1. 1. Department of Mathematics, Xinjiang Normal University, Urumqi 830017, Xinjiang, China;
    2. Department of Mathematics, Xinjiang University, Urumqi 830046, Xinjiang, China
  • Published:2021-11-15

Abstract: The Kronecker product G1⊗G2 of graphs G1 and G2 is the graph with the vertex set V(G1)⊗V(G2), two vertices (u1,v1) and (u2,v2) being adjacent in G1⊗G2 if and only if u1u2∈E(G1) and v1v2∈E(G2). The inverse of Kronecker product of integrally invertible graph is characterized.

Key words: inverse graph, Kronecker product, corona graph, perfect matching

CLC Number: 

  • O157.5
[1] WANG Y, WU B. Proof of a conjecture on connectivity of Kronecker product of graphs[J]. Discrete Mathematics, 2011, 311(21):2563-2565.
[2] GODSIL C D. Inverses of trees[J]. Combinatorica, 1985, 5(1):33-39.
[3] YATES K. Hückel molecular orbital theory[M].[S.l.] : Academic Press, 1978.
[4] HARARY F, MINC H.Which nonnegative matrices are self-inverse?[J]. Math Mag, 1976, 49(2):91-92.
[5] PAVLÍKOVÁ S, ŠEVCOVIC D. On a construction of integrally invertible graphs and their spectral properties[J]. Linear Algebra & Its Applications, 2017, 532:512-533.
[6] AKBARI S, KIRKLAND S J. On unimodular graphs[J]. Linear Algebra and Its Applications, 2007, 421(1):3-15.
[7] NEUMANN M, PATI S. On reciprocal eigenvalue property of weighted trees[J]. Linear Algebra and Its Applications, 2013, 438(10):3817-3828.
[8] FRUCHT R, HARARY F. On the corona of two graphs[J]. Aequationes Mathematicae, 1970, 4(1/2):322-325.
[9] PANDA S K, PATI S. On some graphs which possess inverses[J]. Linear Multilinear Algebra, 2016, 64(7):1445-1459.
[10] YANG Yujun, YE Dong. Inverses of bipartite graphs[J]. Combinatorica, 2018, 38(5):1251-1263.
[11] SIMION R, CAO D-S. Solution to a problem of C.D.Godsil regarding bipartite graphs with unique perfect matching[J]. Combinatorica, 1989, 9(1):85-89.
[12] TIFENBACH R M. Strongly self-dual graphs[J]. Linear Algebra and Its Applications, 2011, 435(12):3151-3167.
[13] MCLEMAN C, MCNICHOLAS E. Graph Invertibility[J]. Graphs and Combinatorics, 2014, 30(4):977-1002.
[14] WEICHESEL P M. The Kornecher product of graphs[J]. Proceedings of the American Mathematical Society, 1962, 13(1):47-52.
[1] WANG Qian. The contractible edges of a spanning tree and a perfect matching in k-connected graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 29-34.
[2] . On the spectrum of matching forcing numbers for bipartite graphs [J]. J4, 2009, 44(12): 30-35.
[3] ZHOU Wei,LIU Xi-kui,WANG Wen-li . Incidence chromatic number and adjacent vertex-distinguishing incidence
chromatic number of hexagonal systems
[J]. J4, 2008, 43(9): 57-62 .
[4] LING Si-Chao, CHENG Wue-Han, WEI Mu-Sheng. On Hermitian solutions to general linear quaternionic matrix equations [J]. J4, 2008, 43(12): 1-4.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!