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| On the Monotonicity of (κ; g, h)-graphs | |
| 作者姓名： | Bao-guang Xu Ping Wang Jian-fang WangInstitute of Policy and Management Chinese Academy of Sciences Beijing China |
| 作者单位： | Bao-guang Xu，Ping Wang，Jian-fang WangInstitute of Policy and Management，Chinese Academy of Sciences，Beijing 100080，ChinaDepartment of Mathematics，Statistics and Computer Science，St. Francis Xavier University，Antigonish，NS，Canada，B2G 2W5Institute of Applied Mathematics，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing，100080，China |
| 基金项目： | the National Natural Science Foundation of China. |
| 摘 要： | A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f(k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A fc-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f(k;h-1,h) |
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