Bounds for the rank of a complex unit gain graph in terms of the independence number
Bounds for the rank of a complex unit gain graph in terms of the independence number
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DOI：
10.1080/03081087.2020.1761768
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发表时间：
2019-09
影响因子：
1.1
通讯作者：
Shengjie He;Rongxia Hao;A. Yu
中科院分区：
文献类型：
--
作者：
Shengjie He;Rongxia Hao;A. Yu
复单位增益图（或-增益图）是由简单图G和增益函数组成的三元组（或简称），简单图G作为单位复数集的基础图，增益函数具有以下性质。的邻接矩阵为，其中，if与相邻，否则。的秩，用表示，是的秩。设和分别为G的独立数和圈数。在本文中，我们证明。并对达到该下界的复单位增益图的性质进行了刻画。此外，还确定了，和的上下界.这些结果推广了无向图、混合图、定向图和符号图的相应结果。
A complex unit gain graph (or -gain graph) is a triple (or for short) consisting of a simple graph G with , as the underlying graph of , the set of unit complex numbers and a gain function with the property that . The adjacency matrix of is , where if is adjacent to and otherwise. The rank of , denoted by , is the rank of . Let and be the independence number and the cyclomatic number of G, respectively. In this paper, we prove that . And the properties of the complex unit gain graphs that attain the lower bound are characterized. Furthermore, the lower and upper bounds on , and are identified. These results generalize the corresponding known results about undirected graphs, mixed graphs, oriented graphs and signed graphs.