JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 53-58.doi: 10.6040/j.issn.1671-9352.0.2018.300

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On the Hermitian-incidence energy of mixed graphs

WANG Wei-zhong, ZHOU Kun-qiang   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2019-06-05

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Abstract: By introducing a new concept— Hermitian-incidence energy(HIE)of a mixed graph M, HIE(M)=∑ni=1(qi)1/2(where qi is the i-th eigenvalues of the Hermitian quasi-Laplacian matrix of M), we mainly point out some bounds to HIE using the number of vertices, edges, and the maximum degrees of M.

Key words: mixed graphs, Hermitian quasi-Laplacian matrix, Hermitian-incidence energy

CLC Number: 

  • O157.5
[1] LIU Jianxi, LI Xueliang. Hermitian-adjacency matrices and Hermitian energies of mixed graphs[J]. Linear Algebra and Its Applications, 2015, 466:182-207.
[2] YU Guihai, QU Hui. Hermitian Laplacian matrix and positive of mixed graphs[J]. Applied Mathematics and Computation, 2015, 269:70-76.
[3] YU Guihai, LIU Xin, QU Hui. Singularity of Hermitian(quasi-)Laplacian matrix of mixed graphs[J]. Applied Mathematics and Computation, 2017, 293:287-292.
[4] JOOYANDEH M R, KIANI D, MIRZAKHAH M. Incidence energy of a graph[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2009, 62(3):561-572.
[5] WANG Weizhong, YANG Dong. Bounds for incidence energy of some graphs[J]. Journal of Applied Mathematics, 2013, 2013:1-7. http://dx.doi.org/10.1155/2013/757542.
[6] WANG Weizhong, LUO Yanfeng, GAO Xing. On incidence energy of some graphs[J]. Ars Combinatoria, 2014, 114:427-436.
[7] GUTMAN I, KIANI D, MIRZAKHAH M. On incidence energy of graphs[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2009, 62(3):573-580.
[8] GUTMAN I, KIANI D, MIRZAKHAH M, et al. On incidence energy of a graph[J]. Linear Algebra and Its Applications, 2009, 431(8):1223-1233.
[9] ZHOU Bo. More upper bounds for the incidence energy[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2010, 64(1):123-128.
[10] ZHANG Jianbin, LI Jianping. New results on the incidence energy of graphs[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2012, 68(3):777-803.
[11] ROJO O, LENES E. A sharp upper bound on the incidence energy of graphs in terms of connectivity[J]. Linear Algebra and Its Applications, 2013, 438(3):1485-1493.
[12] DAS K C, GUTMAN I. On incidence energy of graphs[J]. Linear Algebra and Its Applications, 2014, 446:329-344.
[13] MADEN A D. New bounds on the incidence energy, randic energy and randic estrada index[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2015, 74(2):367-387.
[14] ZHANG Xiaodong, LI Jiongsheng. The Laplacian spectrum of a mixed graph[J]. Linear Algebra and Its Applications, 2002, 353(1/2/3):11-20.
[15] BAPAT R B. Graph and matrices[M]. London: Springer, 2010.
[16] HORN R A, JOHNSON C R. Matrix analysis[M]. 2 eds. New York: Cambridge University Press, 2012.
[17] GUTMAN I, TRINAJSTIC N. Graph theory and molecular orbitals: total π-electron energy of alternant hydrocarbons[J]. Chemical Physics Letters, 1972, 17(4):535-538.
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