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The Nullity of a Graph with Fractional Matching Number by Qian-Qian Chen; Ji-Ming Guo is a Computer Science article available to read on EtoBox.

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Let G be a simple graph with n(G) vertices and e(G) edges. Denoted by η(G) and m \* (G) the nullity and the fractional matching number of G, respectively. The dimension of cycle space of G is defined as c(G) = e(G)n(G) + ω(G), where ω(G) denotes the number of connected components of G. In this paper, we prove that n(G) G, which improves the main results of Wang and Wong (2014) and [11], respectively. Furthermore, all graphs with nullity η(G) = n -2m \* (G) + 2c(G) are determined. We also prove that there is no graph with nullity η(G) = n -2m \* (G) + 2c(G) -1; and for fixed c(G), infinitely many connected graphs with nullity n -2m \* (G) + 2c(G) -k (0 ≤ k ≤ 2c(G), k = 1) are also constructed. As an application of the above results, we also prove that if G is nonsingular, then G has a fractional perfect matching.

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Author

Qian-Qian Chen; Ji-Ming Guo

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Computer Science (Physical Sciences)