一类θ-图的邻点可区别关联着色

The Adjacent Vertex Distinguishable Incidence Coloring of A Kind of θ-Graphs

用反证法和枚举法研究了一种θ-图的邻点可区别关联着色,并确定θ-图的邻点可区别关联色数。对于θ-图,若uv∈E(θ),或N1=N2=N3=1,或N1=N2=N3=2,或uv E(θ)且N1,N2和N3三者中有一个等于1,一个等于2时,则χAI(θ)=5;否则,χAI(θ)=4。

The reduction to absurdity and enumerative algorithm were used to study the adjacent vertex distinguishable incidence coloring of a kind of θ-graphs and determine the adjacent vertex distinguishable incidence chromatic number in this paper.For θ-graphs,if uv∈E（θ）,orN1=N2=N3=1,or N1=N2=N3=2,or uvE（θ） and if one equals 1 and another equals 2 among N1,N2 and N3,then χAI（θ）=5;otherwise χAI（θ）=4.