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Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers
Joint Authors
Jumnongnit, Patcharapan
Nakprasit, Kittikorn
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-07
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
Let G be a graph and ϕ:V(G)∪E(G)→{1,2,3,…,k} be a k-total coloring.
Let w(v) denote the sum of color on a vertex v and colors assigned to edges incident to v.
If w(u)≠w(v) whenever uv∈E(G), then ϕ is called a neighbor sum distinguishing total coloring.
The smallest integer k such that G has a neighbor sum distinguishing k-total coloring is denoted by tndi∑ (G).
In 2014, Dong and Wang obtained the results about tndi∑ (G) depending on the value of maximum average degree.
A k-assignment L of G is a list assignment L of integers to vertices and edges with L(v)=k for each vertex v and L(e)=k for each edge e.
A total-L-coloring is a total coloring ϕ of G such that ϕ(v)∈L(v) whenever v∈V(G) and ϕ(e)∈L(e) whenever e∈E(G).
We state that G has a neighbor sum distinguishing total-L-coloring if G has a total-L-coloring such that w(u)≠w(v) for all uv∈E(G).
The smallest integer k such that G has a neighbor sum distinguishing total-L-coloring for every k-assignment L is denoted by Ch∑ ′′(G).
In this paper, we strengthen results by Dong and Wang by giving analogous results for Ch∑ ′′(G).
American Psychological Association (APA)
Jumnongnit, Patcharapan& Nakprasit, Kittikorn. 2017. Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers. International Journal of Mathematics and Mathematical Sciences،Vol. 2017, no. 2017, pp.1-4.
https://search.emarefa.net/detail/BIM-1167758
Modern Language Association (MLA)
Jumnongnit, Patcharapan& Nakprasit, Kittikorn. Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers. International Journal of Mathematics and Mathematical Sciences No. 2017 (2017), pp.1-4.
https://search.emarefa.net/detail/BIM-1167758
American Medical Association (AMA)
Jumnongnit, Patcharapan& Nakprasit, Kittikorn. Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers. International Journal of Mathematics and Mathematical Sciences. 2017. Vol. 2017, no. 2017, pp.1-4.
https://search.emarefa.net/detail/BIM-1167758
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1167758