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Arika I. Kristiana
CGANT University of Jember; Mathematics Edu. Depart. University of Jember
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On The Total r-dynamic Coloring of Edge Comb Product graph G D H Dwi Agustin Retno Wardani; Dafik Dafik; Antonius C. Prihandoko; Arika I. Kristiana
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Given that two natural numbers r, k. By a proper total k-coloring of a graph G, we mean a map c : V (G) ∪ E(G) → {1, 2, . . . , k}, such that any two adjacent vertices and incident edges receive different colors. A total r-dynamic coloring is a proper k-coloring c of G, such that ∀v ∈ V (G), |c(N(v))| ≥ min{r, d(v) + |N(v)|} and ∀e ∈ E(G), |c(N(e))| ≥ min{r, d(v) + d(u)}. The total r-dynamic chromatic number, written as χ ”r(G), is the minimum k such that G has an r-dynamic total k-coloring. A total r-dynamic coloring is a natural extension of r-dynamic coloring in which we consider more condition of the concept, namely not only assign a color on the vertices as well as on the edges. Consequently, this study will be harder. In this paper, we will initiate to analyze a total r-dynamic of an edge comb product of two graphs, denoted by H D K, where H is path graph and K is any special graph. The result shows that the total r-dynamic chromatic number of Pn D K.
Co-Authors Antonius C. Prihandoko D. Dafik Dwi Agustin Retnowardani