In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number...In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree.展开更多
Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw...Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, whereC（u）={f（u）}∪{f（uv）｜uv∈E（G）}.Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.展开更多
文摘In this paper, we present a new concept of the adjacent-vertex-distinguishing total coloring of graphs (briefly, AVDTC of graphs) and, meanwhile, have obtained the adjacent-vertex-distinguishing total chromatic number of some graphs such as cycle, complete graph, complete bipartite graph, fan, wheel and tree.
基金the Natural Science Foundation of Gansu Province （No. 3ZS051-A25-025） the Foundation of Gansu Provincial Department of Education （No. 0501-03）.
文摘Let G = （V, E） be a simple connected graph, and ｜V（G）｜ ≥ 2. Let f be a mapping from V（G） ∪ E（G） to {1,2…, k}. If arbitary uv ∈ E（G）,f（u） ≠ f（v）,f（u） ≠ f（uv）,f（v） ≠ f（uv）; arbitary uv, uw ∈ E（G）（v ≠ w）, f（uv） ≠ f（uw）;arbitary uv ∈ E（G） and u ≠ v, C（u） ≠ C（v）, whereC（u）={f（u）}∪{f（uv）｜uv∈E（G）}.Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G（k-AVDTC of G for short）. The number min{k｜k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat（G）. In this paper we prove that if △（G） is at least a particular constant and δ ≥32√△ln△, then χat（G） ≤ △（G） ＋ 10^26 ＋ 2√△ln△.
