The neighbor expanded sum distinguishing index of Halin graphs

Jingjing Huo; Wai Chee Shiu; Weifan Wang

The neighbor expanded sum distinguishing index of Halin graphs

Jingjing Huo, Wai Chee Shiu^*, Weifan Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

Let G = (V, E) be a graph. A total k-weighting c of G is a function c: V(G) ∪ E(G) → {1,2,...,k}. For x ∈ V(G), define w(x) = Σ(c(xy)+c(y)). A total k-weighting c of G is called neighbor expanded sum distinguishing (nesd for short) if w(u) ≠ w(v) for every uv ∈ E(G). The smallest value of k for which such a nesd total k-weighting of G exists is called the neighbor expanded sum distinguishing index of G, denoted by nesd_t(G). In this paper, we prove that nesd_t(G) ≤ 3 for any Halin graph G. Furthermore, nesd_t(G) = 2 for the cubic Halin graphs G.

Original language	English
Pages (from-to)	63-73
Number of pages	11
Journal	Ars Combinatoria
Volume	141
Publication status	Published - Oct 2018

Scopus Subject Areas

General Mathematics

User-Defined Keywords

Halin graphs
Neighbor expanded sum distinguishing index
Total weighting

Cite this

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title = "The neighbor expanded sum distinguishing index of Halin graphs",

abstract = "Let G = (V, E) be a graph. A total k-weighting c of G is a function c: V(G) ∪ E(G) → {1,2,...,k}. For x ∈ V(G), define w(x) = Σ(c(xy)+c(y)). A total k-weighting c of G is called neighbor expanded sum distinguishing (nesd for short) if w(u) ≠ w(v) for every uv ∈ E(G). The smallest value of k for which such a nesd total k-weighting of G exists is called the neighbor expanded sum distinguishing index of G, denoted by nesdt(G). In this paper, we prove that nesdt(G) ≤ 3 for any Halin graph G. Furthermore, nesdt(G) = 2 for the cubic Halin graphs G.",

keywords = "Halin graphs, Neighbor expanded sum distinguishing index, Total weighting",

author = "Jingjing Huo and Shiu, {Wai Chee} and Weifan Wang",

note = "Funding Information: Research was done while the first author visited Department of Mathematics, Hong Kong Baptist University in 2015. Partially supported by NSFC (No. 11371328, No. 11501161, No. 11701136) and NSFHB (No. A2016402164), Tianjin Research Program of Application Foundation and Advanced Technology (No. 14JCYBJC43100), National Natural Science Foundation of China (No. 11601391).",

year = "2018",

month = oct,

language = "English",

volume = "141",

pages = "63--73",

journal = "Ars Combinatoria",

issn = "0381-7032",

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T1 - The neighbor expanded sum distinguishing index of Halin graphs

AU - Huo, Jingjing

AU - Shiu, Wai Chee

AU - Wang, Weifan

N1 - Funding Information: Research was done while the first author visited Department of Mathematics, Hong Kong Baptist University in 2015. Partially supported by NSFC (No. 11371328, No. 11501161, No. 11701136) and NSFHB (No. A2016402164), Tianjin Research Program of Application Foundation and Advanced Technology (No. 14JCYBJC43100), National Natural Science Foundation of China (No. 11601391).

PY - 2018/10

Y1 - 2018/10

N2 - Let G = (V, E) be a graph. A total k-weighting c of G is a function c: V(G) ∪ E(G) → {1,2,...,k}. For x ∈ V(G), define w(x) = Σ(c(xy)+c(y)). A total k-weighting c of G is called neighbor expanded sum distinguishing (nesd for short) if w(u) ≠ w(v) for every uv ∈ E(G). The smallest value of k for which such a nesd total k-weighting of G exists is called the neighbor expanded sum distinguishing index of G, denoted by nesdt(G). In this paper, we prove that nesdt(G) ≤ 3 for any Halin graph G. Furthermore, nesdt(G) = 2 for the cubic Halin graphs G.

AB - Let G = (V, E) be a graph. A total k-weighting c of G is a function c: V(G) ∪ E(G) → {1,2,...,k}. For x ∈ V(G), define w(x) = Σ(c(xy)+c(y)). A total k-weighting c of G is called neighbor expanded sum distinguishing (nesd for short) if w(u) ≠ w(v) for every uv ∈ E(G). The smallest value of k for which such a nesd total k-weighting of G exists is called the neighbor expanded sum distinguishing index of G, denoted by nesdt(G). In this paper, we prove that nesdt(G) ≤ 3 for any Halin graph G. Furthermore, nesdt(G) = 2 for the cubic Halin graphs G.

KW - Halin graphs

KW - Neighbor expanded sum distinguishing index

KW - Total weighting

UR - http://www.combinatoire.ca/ArsCombinatoria/Vol141.html

UR - http://www.scopus.com/inward/record.url?scp=85056180327&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:85056180327

SN - 0381-7032

VL - 141

SP - 63

EP - 73

JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

The neighbor expanded sum distinguishing index of Halin graphs

Abstract

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