Interval Total Colorings Of Several Kinds Of Graphs

An interval total t-coloring of a graph G is a total coloring of G with colors 1,2,...,t such that all colors are used,and the edges incident to each vertex u together with u are colored by dG(u)+1 consecutive colors,where dG(u)is the degree of a vertex u in G. A graph G is interval total colorable if it has an interval total t-coloring for some positive integer t. Let (?)-∪t≥1(?)t,where (?)t(t≥1)denote the set of the t-interval total colorable graphs. For any G∩(?),the least and the greatest values of t for which G has an interval total t-coloring are denoted by wτ,(G) and Wτ(G),respectively.In this paper,we study interval total colorings of several kinds of graphs. First of all we prove that the generalized θ-graph θm is interval total colorable,and show that ωτ(θm)-m+1 and Wτ(θm)=l+l’+m, where l is the length of a longest(u,v)-path in θm,l’ is the length of the longest(u,v)-path other than the above-mentioned(u,v)-path in θm,for θm,ωτ(θm)-m+1,Wτ(θm)-l+l’+m Then we show that the generalized Mycielski graph of path Pn(μm(Pn)) is interval total colorable,for m≥1,n≥2, By the end we prove that 3-regular Halin graph H is interval total colorable and...