Neighbor sum distinguishing total choosability of IC-planar graphs

Abstract

Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane such that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. A proper total-kcoloring of a graph G is a mapping c : V (G) ∪ E(G) → {1, 2,. .. , k} such that any two adjacent elements in V (G) ∪ E(G) receive different colors. Let

Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs without Theta Graphs Θ2,1,2

“…Wang et al [11] confirmed Conjecture 2 for every planar graph G with maximum degree ∆(G) ≥ 8 but without theta graphs Θ 2,1,2 . Song et al [12] discussed the NSD total L-coloring of any IC-planar graph and obtained the following theorem.…”