More skew-equienergetic digraphs

Document Type : Original paper

Authors

University of Mysore

Abstract

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.

Keywords

Main Subjects


[1] C. Adiga, R. Balakrishnan, and W. So, The skew energy of a digraph, Linear Algebra Appl. 432 (2010), 1825–1835.
[2] C. Adiga, B. R. Rakshith, and W. So, On the mixed adjacency matrix of a mixed graph, Linear Algebra Appl. 495 (2016), 223–241.
[3] A. Anuradha, R. Balakrishnan, X. Chen, X. Li, H. Lian, and W. So, Skew spectra of oriented bipartite graphs, Electronic J. Combin. 4 (2013), P#18.
[4] R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004), 287–295.
[5] R. B. Bapat, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc. 1 (2004), 129–132.
[6] X. Chen, X. Li, and H. Lian, 4-regular oriented graphs with optimum skew energy, Linear Algebra Appl. 439 (2013), 2948–2960.
[7] D. Cvetković, M. Doob, and H. Sachs, Spectra of graphs: Theory and application, Academic press New York, 1980.
[8] S. C. Gong, X. Li, G. Xu, I. Gutman, and B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 74 (2015), 321–332.
[9] S. C. Gong and G. H. Xu, 3-regular oriented graphs with optimum skew energy, Linear Algebra Appl. 436 (2012), 465–471.
[10] I. Gutman, The energy of a graph, Ber. Math. Statist. sekt. Forschungsz. Graz. 103 (1978), 1–22.
[11] , The energy of a graph: old and new results, Algebraic Combinatorics and Applications, ed(s), A. Betten, A. Kohnert, R. Laue, A. Wassermann, Berlin: Springer 103 (2000), 196–211.
[12] , Topology and stability of conjugated hydrocarbons. the dependence of total π-electron energy on molecular topology, J. Serb. Chem. Soc. 70 (2005), 441–456.
[13] Y. Hou and T. Lei, Characteristic polynomials of skew-adjacency matrices of oriented graphs, The Electronic J. Combin. 18 (2011), #156.
[14] G. Indulal and A. Vijayakumar, On a pair of equienergetic graphs, MATCH. Commun. Math. Comput. Chem. 55 (2006), 83–90.
[15] J. Li, X. Li, and H. Lian, Extremal skew energy of digraphs with no even cycles, Trans. Comb. 3 (2014), 37–49.
[16] X. Li and H. Lian, A survey on the skew energy of oriented graphs, arXiv:1304.5707.
[17] X. Li, Y. Shi, and I. Gutman, Graph energy, Springer New York, 2012.
[18] J. Liu and B. Liu, On a pair of equienergetic graphs, MATCH. Commun. Math. Comput. Chem. 59 (2008), 275–278.
[19] H. S. Ramane, I. Gutman, H. B. Walikar, and S. B. Halkarni, Equienergetic complement graphs, Kragujevac J. Sci. 27 (2005), 67–74.
[20] H. S. Ramane, K. C. Nandeesh, I. Gutman, and X. Li, Skew equienergetic digraphs, Trans. Comb. 5 (2016), 15–23.
[21] H. S. Ramane and H. B. Walikar, Construction of equienergetic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 203–210.
[22] L. Xu and Y. Hou, Equienergetic bipartite graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 363–370.