Abstract
The non-zero component graph of a vector space with finite dimension over a finite field F is the graph \(G~ = ~\left( {V,E} \right)\), where vertices of G are the non-zero vectors in V, two of which are adjacent if they have at least one basis vector with non-zero coefficient common in their basic representation. In this paper, we discuss certain properties of the non-zero component graphs of vector spaces with finite dimension over finite fields and their graph invariants.
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References
Bondy JA, Murty USR (2008) Graph theory. Springer, New York
Harary F (1967) Graph theory and theoretical physics. Academic Press, Cambridge
West DB (2001) Introduction to graph theory. Prentice hall, Upper Saddle River
Beineke LW, Wilson RJ, Cameron PJ (2004) Topics in algebraic graph theory, vol 102. Cambridge University Press, Cambridge
Biggs N (1993) Algebraic graph theory. Cambridge University Press, Cambridge
Godsil C, Royle GF (2001) Algebraic graph theory, vol 207. Springer Science & Business Media, Berlin
Beezer R A (2015) A first course in linear algebra. Independent
Hoffman K, Kunze R (2015) Linear algebra. Pearson India, New Delhi
Strang G (1993) Introduction to linear algebra, vol 3. Wellesley-Cambridge Press, Wellesley
Das A (2016) Nonzero component graph of a finite dimensional vector space. Comm Algebra 44(9):3918–3926
Kathiresan K, Marimuthu G (2010) A study on radial graphs. Ars Combin 96:353–360
Das A (2017) On non-zero component graph of vector spaces over finite fields. J Algebra Appl 16(01), 1750007:1–10
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Mathew, V.M., Naduvath, S. (2021). Some New Results on Non-zero Component Graphs of Vector Spaces Over Finite Fields. In: Shukla, S., Unal, A., Kureethara, J.V., Mishra, D.K., Han, D.S. (eds) Data Science and Security. Lecture Notes in Networks and Systems, vol 290. Springer, Singapore. https://doi.org/10.1007/978-981-16-4486-3_29
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DOI: https://doi.org/10.1007/978-981-16-4486-3_29
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