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| 一类含有4-圈的单圈图的一般点可区别全染色 |
| General Vertex-Distinguishing Total Colorings of a family of Unicyclic Graphs including C4 |
| 投稿时间：2016-06-21 修订日期：2016-07-14 |
| DOI： |
| 中文关键词: 单圈图 一般全染色 一般点可区别全染色 一般点可区别全色数. |
| 英文关键词: unicyclic graphs general total coloring general vertex-distinguishing total coloring general vertex-distinguishing total chromatic number. |
| 基金项目:国家自然科学基金资助项目(61163037, 61163054, 11261046)和宁夏回族自治区百人计划资助项目 |
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| 中文摘要: |
| 设G为简单图. G的一般全染色是指若干种颜色对图G的全体顶点及边的一个分配.
设f为G的一个一般全染色, x为G的一个顶点, 将在f下x的颜色及与x关联的边的颜色所构成的集合
记为Cf (x)或C(x), 称之为顶点x在f下的色集合, 即C(x) = {f(xu)|xu ∈ E}∪{f(x)}: 设f是G的一
个一般全染色, 若对图G的任意两个不同的顶点u, v, 有C(u)?=C(v), 则f称为图G的一般点可区别全
染色(GVDTC). 对图G进行一般点可区别全染色所需要的最少颜色数称为G的一般点可区别全色
数. 本文探讨了一类含有4?圈的单圈图的一般点可区别全染色, 并确定了它的一般点可区别全色
数. |
| 英文摘要: |
| Let G be a simple graph. A general total coloring is an assignment of several
colors to all vertices and edges of G. Let Cf (x) or simply C(x) be the set of colors of vertex x and
edges incident with x under f, i.e., C(x) = {f(xu)|xu ∈ E}∪{f(x)}; which is called the color
set of vertex x under f. For a general total coloring f of G, if C(u)?=C(v) for any two different
vertices u and v of G, then f is called a general vertex-distinguishing total coloring of G (or
GVDTC of G for short). The minimum number of colors required in a GVDTC is the general
vertex-distinguishing total chromatic number. The general vertex-distinguishing total colorings
of a family of Unicyclic Graphs including C4 is discussed and its general vertex-distinguishing
total chromatic numbers is determined in this paper. |
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