Neighbor sum distinguishing total colorings of planar graphs with maximum degree Δ
نویسندگان
چکیده
منابع مشابه
Neighbor sum distinguishing edge colorings of graphs with small maximum average degree
A proper edge-k-coloring of a graph G is an assignment of k colors 1, 2, · · · , k to the edges of G such that no two adjacent edges receive the same color. A neighbor sum distinguishing edge-k-coloring of G is a proper edge-k-coloring of G such that for each edge uv ∈ E(G), the sum of colors taken on the edges incident with u is different from the sum of colors taken on the edges incident with...
متن کاملTotal colorings of planar graphs with large maximum degree
It is proved that a planar graph with maximum degree ∆ ≥ 11 has total (vertex-edge) chromatic number ∆ + 1. c © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997
متن کاملTotal Colorings of Planar Graphs with Small Maximum Degree
Let G be a planar graph of maximum degree ∆ and girth g, and there is an integer t(> g) such that G has no cycles of length from g+1 to t. Then the total chromatic number of G is ∆+1 if (∆,g, t) ∈ {(5,4,6),(4,4,17)}; or ∆ = 3 and (g, t) ∈ {(5,13),(6,11),(7,11), (8,10),(9,10)}, where each vertex is incident with at most one g-cycle. 2010 Mathematics Subject Classification: 05C15
متن کاملOn the Neighbor Sum Distinguishing Index of Planar Graphs
Let c be a proper edge colouring of a graph G = (V,E) with integers 1, 2, . . . , k. Then k ≥ ∆(G), while by Vizing’s theorem, no more than k = ∆(G)+ 1 is necessary for constructing such c. On the course of investigating irregularities in graphs, it has beenmoreover conjectured that only slightly larger k, i.e., k = ∆(G) + 2 enables enforcing additional strong feature of c, namely that it attri...
متن کاملTotal Colorings of $F_5$-free Planar Graphs with Maximum Degree 8
The total chromatic number of a graph G, denoted by χ′′(G), is the minimum number of colors needed to color the vertices and edges of G such that no two adjacent or incident elements get the same color. It is known that if a planar graph G has maximum degree ∆ > 9, then χ′′(G) = ∆ + 1. The join K1 ∨ Pn of K1 and Pn is called a fan graph Fn. In this paper, we prove that if G is an F5-free planar...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.03.013