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arXiv · 1303.4971

A characterization of graphs with 3-coverings and the evaluation of the 3-covering energy of star graphs with m rays of length 2

Paul August Winter
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Abstract

The smallest set Q of vertices of a graph G, such that every path on 3 vertices, has at least one vertex in Q, is a minimum 3-covering of G. By attaching loops of weight 1 to the vertices of G we can find the eigenvalues associated with G, and hence the minimum 3-covering energy of G. In this paper we characterize graphs with 3-coverings in terms of non-Q-covered edges, and we determine the minimum 3-covering energy of a star graph with m rays each of length 2.

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Paul August Winter. 2013-03-20. A characterization of graphs with 3-coverings and the evaluation of the 3-covering energy of star graphs with m rays of length 2. https://arxiv.org/abs/1303.4971

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