JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (3): 78-84.doi: 10.6040/j.issn.1671-9352.0.2021.516

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Hermitian-general Randic quasi-Laplacian matrix and Hermitian-general Randic incidence energy of mixed graphs

ZHANG Hai-dong, WANG Wei-zhong*   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-03-15

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Abstract: The Hermitian-general Randic quasi-Laplacian matrix and the Hermitian-general Randic incidence matrix of mixed graphs are introduced, and the relationship between them is given; some properties of Hermitian-general Randic quasi-Laplacian matrix of mixed graphs are characterized. Moreover, the concept of general Randic incidence energy of undirected graphs is extended to the Hermitian-general Randic incidence energy of mixed graphs, and the upper and lower bounds of the Hermitian-general Randic incidence energy of n order mixed graphs are obtained.

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

CLC Number: 

  • O157.5
[1] 刘木伙, 柳柏濂. 图谱的极值理论[M]. 广州:广东科技出版社, 2017. LIU Muhuo, LIU Bolian. Extremal theory of graph spectrum[M]. Guangzhou: Guangdong Science and Technology Press, 2017.
[2] CHUNG F R K. Spectral graph theory[M]. Providence, Rhode Island: American Mathematical Society, 1997.
[3] RANDIC M. On characterization of molecular branching[J]. Journal of the American Chemical Society, 1975, 97(23):6609-6615.
[4] BOLLOBÁS B, ERDÖS P. Graphs of extremal weights[J]. Ars Combinatoria Waterloo Then Winnipeg, 1998, 50:225-233.
[5] GU Ran, HUANG Fei, LI Xueliang. General Randic matrix and general Randic energy[J]. Transactions on Combinatorics, 2014, 3(3):21-33.
[6] LU Yong, WANG Ligong, ZHOU Qiannan. Hermitian-Randic matrix and Hermitian-Randic energy of mixed graphs[J]. Journal of Inequalities and Applications, 2017, 2017(1):54.
[7] NIKIFOROV V. The energy of graphs and matrices[J]. Journal of Mathematical Analysis and Applications, 2007, 326(2):1472-1475.
[8] JOOYANDEH M, KIANI D, MIRZAKHAH M. Incidence energy of a graph[J]. MATCH Communications in Mathematical and in Computer Chemistry, 2009, 62(3):561-572.
[9] GU Ran, HUANG Fei, LI Xueliang. Randic incidence energy of graphs[J]. Transactions on Combinatorics, 2014, 3(4):1-9.
[10] LIU Ruifang, SHIU W C. General Randic matrix and general Randic incidence matrix[J]. Discrete Applied Mathematics, 2015, 186:168-175.
[11] 王维忠, 周琨强. 混合图的埃尔米特-关联能量[J]. 山东大学学报(理学版), 2019, 54(6):53-58. WANG Weizhong, ZHOU Kunqiang. On the Hermitian-incidence energy of mixed graphs[J]. Journal of Shandong University(Natural Science), 2019, 54(6):53-58.
[12] SARMA D. Minors of Hermitian(quasi-)Laplacian matrix of a mixed graph[J]. Linear and Multilinear Algebra, 2020, 68(11):2157-2169.
[13] YU Guihai, LIU Xin, QU Hui. Singularity of Hermitian(quasi-)Laplacian matrix of mixed graphs[J]. Applied Mathematics and Computation, 2017, 293:287-292.
[14] YU Guihai, QU Hui. Hermitian Laplacian matrix and positive of mixed graphs[J]. Applied Mathematics and Computation, 2015, 269:70-76.
[1] WANG Wei-zhong, ZHOU Kun-qiang. On the Hermitian-incidence energy of mixed graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 53-58.
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