Note for Constructing Minimum Integrity Trees with Given Order and Maximum Degree
Y Li, X Qin, F Li, W Li - Journal of Interconnection Networks, 2020 - World Scientific
Y Li, X Qin, F Li, W Li
Journal of Interconnection Networks, 2020•World ScientificFor a given graph G=(V, E), its integrity is defined as I (G)= min X⊂ V {| X|+ m (G− X)}, where
m (G− X) denote the order of the largest component of G− X. In [9], authors discuss the
minimum integrity of tree with given order and the maximum degree. In this paper, we point
that the result in [9] is flawed and by elementary method characterize the structure of the
minimum integrity tree and thus correct Theorem 4.1 in [9]. Finally, we give the construction
method of this kind of extremal graph.
m (G− X) denote the order of the largest component of G− X. In [9], authors discuss the
minimum integrity of tree with given order and the maximum degree. In this paper, we point
that the result in [9] is flawed and by elementary method characterize the structure of the
minimum integrity tree and thus correct Theorem 4.1 in [9]. Finally, we give the construction
method of this kind of extremal graph.
For a given graph G = (V, E), its integrity is defined as I(G) = minX⊂V {|X|+m(G−X)}, where m(G−X) denote the order of the largest component of G−X. In [9], authors discuss the minimum integrity of tree with given order and the maximum degree. In this paper, we point that the result in [9] is flawed and by elementary method characterize the structure of the minimum integrity tree and thus correct Theorem 4.1 in [9]. Finally, we give the construction method of this kind of extremal graph.
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