| 直径为4的树的IC-着色和IC-指数 |
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| 引用本文： | 姜臻颖,王力工. 直径为4的树的IC-着色和IC-指数[J]. 数学的实践与认识, 2017, 0(15): 307-312 |
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| 作者姓名： | 姜臻颖 王力工 |
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| 作者单位： | 西北工业大学 理学院应用数学系,陕西 西安,7100072 |
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| 基金项目： | 国家自然科学基金(11171273)，国家大学生创新创业训练计划项目(201310699069) |
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| 摘 要： | 根据Salehi等人在Discrete Mathematics上提出的图的IC-指数及极大IC-着色的相关概念,研究了直径为4的树T=T(m_1,m_2,…,m_s)的IC=着色问题·得到了当2≤<_1,m_2,…,m_s-1≤m_s,s≥2时,树T的IC-指数为Π_j=1~s(2~mj+1)+(2m,+1),其极大IC-着色有|π|种,其中|π|为m_1,同_2,…m_…s-1的全排列数.这为确定图的IC-指数提供了一般方法.
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| 关 键 词： | IC-着色 IC-指数 极大IC-着色 直径为4的树 |
IC-colorings and IC-indices of Trees of Diameter Four |
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| JIANG Zhen-ying,WANG Li-gong. IC-colorings and IC-indices of Trees of Diameter Four[J]. Mathematics in Practice and Theory, 2017, 0(15): 307-312 |
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| Authors: | JIANG Zhen-ying WANG Li-gong |
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| Abstract: | With the concepts of IC-index and maximum IC-colorings of graphs put forward by Salehi etc.in Discrete Mathematics,the IC-index of the tree T =T (m1,m2,...,ms) of diameter four is studied.When 2 ≤ m1,m2,...,ms-1 ≤ ms,s ≥ 2,it is proven that the IC-index of the tree T is (2 + 1) + ∏sj=1 (2mj + 1) and there are |π| kinds of maximum IC-coloring of the tree T,where |π| represents the number of all permutations of positive integers m1,m2,...,ms-1.It also provide a method to find IC-indices of graphs. |
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| Keywords: | IC-coloring IC-index Maximum IC-coloring Trees of diameter four |
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