Non-zero component union graph of a finite-dimensional vector space |
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Authors: | Angsuman Das |
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Institution: | 1. Department of Mathematics, St. Xavier’s College, Kolkata, Kolkata, India.angsumandas@sxccal.edu |
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Abstract: | In this paper, we introduce a graph structure, called non-zero component union graph on finite-dimensional vector spaces. We show that the graph is connected and find its domination number, clique number and chromatic number. It is shown that two non-zero component union graphs are isomorphic if and only if the base vector spaces are isomorphic. In case of finite fields, we study the edge-connectivity and condition under which the graph is Eulerian. Moreover, we provide a lower bound for the independence number of the graph. Finally, we come up with a structural characterization of non-zero component union graph. |
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Keywords: | Basis independent set graph |
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