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New results on Orthogonal Component Graphs of Vector Spaces over $\mathbb{Z}_p$ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 9، شماره 3، آذر 2024، صفحه 485-495 اصل مقاله (387.07 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28034.1422 | ||
| نویسندگان | ||
| Vrinda Mary Mathew؛ Sudev Naduvath* ؛ Thadathil Joseph Varghese | ||
| Department of Mathematics, CHRIST (Deemed to be University), Bangalore-560029, Karnataka, India | ||
| چکیده | ||
| A new concept known as the orthogonal component graph associated with a finite-dimensional vector space over a finite field has been recently added as another class of algebraic graphs. In these graphs, the vertices will be all the possible non-zero linear combinations of orthogonal basis vectors. Any two vertices will be adjacent if the corresponding vectors are orthogonal. In this paper, we discuss the various colorings and structural properties of orthogonal component graphs. | ||
| کلیدواژهها | ||
| Orthogonal component graph؛ graph coloring؛ planarity؛ unicyclic graphs؛ centrality measures | ||
| مراجع | ||
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[1] L.W. Beineke, R.J. Wilson, and P.J. Cameron, Topics in Algebraic Graph Theory, vol. 102, Cambridge University Press, 2004.
[2] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New York, 2008.
[3] G. Chartrand, T.W. Haynes, M.A. Henning, and P. Zhang, From Domination to Coloring: Stephen Hedetniemi’s graph theory and beyond, Springer Nature, 2019.
[4] A. Das, Non-zero component graph of a finite dimensional vector space, Comm. Algebra 44 (2016), no. 9, 3918–3926.
[5] A. Das, Non-zero component union graph of a finite-dimensional vector space, Linear Multilinear Algebra 65 (2017), no. 6, 1276–1287. https://doi.org/10.1080/03081087.2016.1234577 [6] A. Das, On non-zero component graph of vector spaces over finite fields, J. Algebra Appl. 16 (2017), no. 1, Article ID: 1750007. https://doi.org/10.1142/S0219498817500074 [7] A. Das, On subspace inclusion graph of a vector space, Linear Multilinear Algebra 66 (2018), no. 3, 554–564. https://doi.org/10.1080/03081087.2017.1306016 [8] C.D. Godsil and M.W. Newman, The automorphism group and fixing number of orthogonality graph over a vector space, SIAM J. Discrete Math. 22 (2008), no. 2, 683–692.
[9] V.M. Mathew and S. Naduvath, On non-zero component graphs of finite dimensional vector spaces, Lecture Notes Netw. Syst. (2021).
[10] V.M. Mathew and S. Naduvath, Coloring of non-zero component graphs, Communicated (2022).
[11] V.M. Mathew, S. Naduvath, and I.N. Cangul, Some vertex degree-based topological indices of non-zero component graphs, Communicated (2022).
[12] V.M. Mathew, S. Naduvath, and T.V. Joseph, On orthogonal component graphs of vector spaces over the field $Z_p$, Proyecciones J. Math. (to appear).
[13] S. Ou and Y. Tan, The automorphism group and fixing number of orthogonality graph over a vector space, J. Algebra Appl. 20 (2021), no. 12, Article ID: 2350013. https://doi.org/10.1142/S0219498823500135 [14] G. Strang, Introduction to Linear Algebra, vol. 3, Wellesley-Cambridge Press Wellesley, MA, 1993.
[15] D.B. West, Introduction to Graph Theory, Prentice hall Upper Saddle River, 2001. | ||
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