On (p,1)-total labelling of some 1-planar graphs

On total colorings of 1-planar graphs

A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we confirm the total-coloring conjecture for 1-planar graphs with maximum degree

Some Results on List Total Colorings of Planar Graphs

Let G be a planar graph with maximum degree Δ. In this paper, it is proved that if Δ ≥ 9, then G is total-(Δ+2)-choosable. Some results on list total coloring of G without cycles of specific lengths are given.

(d, 1)-total Labelling of Planar Graphs with Large Girth and High Maximum Degree

The (d, 1)-total number λ T d (G) of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G so that no two adjacent vertices have the same label, no two incident edges have the same label and the difference between the labels of a vertex and its incident edges is at least d. This notion was introduced in Havet. In this talk, we present ou...

On the edge and total GA indices of some graphs

List (d,1)-total labelling of graphs embedded in surfaces

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we consider the list version of (d,1)-total labelling of graphs. Let G be a graph embedded in a surface with Euler characteristic ε whose maximum degree ∆(G) is sufficiently large. We prove that the (d,1)-total choosability C d,1(G) of G is at most ∆(G) + 2d.