Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2017, Article ID 5897049, 4 pages
https://doi.org/10.1155/2017/5897049
Research Article

Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Correspondence should be addressed to Kittikorn Nakprasit; moc.liamtoh@kantik

Received 31 May 2017; Accepted 4 October 2017; Published 7 November 2017

Academic Editor: Daniel Simson

Copyright © 2017 Patcharapan Jumnongnit and Kittikorn Nakprasit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a graph and be a -total coloring. Let denote the sum of color on a vertex and colors assigned to edges incident to . If whenever , then is called a neighbor sum distinguishing total coloring. The smallest integer such that has a neighbor sum distinguishing -total coloring is denoted by . In 2014, Dong and Wang obtained the results about depending on the value of maximum average degree. A -assignment of is a list assignment of integers to vertices and edges with for each vertex and for each edge . A total--coloring is a total coloring of such that whenever and whenever . We state that has a neighbor sum distinguishing total--coloring if has a total--coloring such that for all . The smallest integer such that has a neighbor sum distinguishing total--coloring for every -assignment is denoted by . In this paper, we strengthen results by Dong and Wang by giving analogous results for .