TY - JOUR

T1 - Local irregularity chromatic number of vertex shackle product of graphs

AU - Umilasari, R.

AU - Susilowati, L.

AU - Slamin,

N1 - Funding Information:
We gratefully acknowledge the support from Universitas Muhammadiyah Jember and DRPM Kemristekdikti through World Class Research grant year 2019.
Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2020/5/28

Y1 - 2020/5/28

N2 - Local irregular vertex labeling is one of graph labeling type that can be used as a tool for graph coloring. A mapping l is called local irregular vertex labeling if there are: (i) a mapping as vertex irregular k -labeling and a weight , for every where ; and (ii) apt(l) = min{max{li }. Thus, the labeling l induces a proper vertex coloring of G where the vertex v is assigned the color w(v). The local irregular chromatic number of G, denoted by is the minimum cardinality of the largest label over all such local irregular vertex labeling. In this paper, we determine the local irregular chromatic number of a vertex shackle product of graphs. The vertex shackle products of graphs, denoted by Shack (G, v, k), is the graph constructed from k copies of connected graph G and v as the linkage vertex.

AB - Local irregular vertex labeling is one of graph labeling type that can be used as a tool for graph coloring. A mapping l is called local irregular vertex labeling if there are: (i) a mapping as vertex irregular k -labeling and a weight , for every where ; and (ii) apt(l) = min{max{li }. Thus, the labeling l induces a proper vertex coloring of G where the vertex v is assigned the color w(v). The local irregular chromatic number of G, denoted by is the minimum cardinality of the largest label over all such local irregular vertex labeling. In this paper, we determine the local irregular chromatic number of a vertex shackle product of graphs. The vertex shackle products of graphs, denoted by Shack (G, v, k), is the graph constructed from k copies of connected graph G and v as the linkage vertex.

UR - http://www.scopus.com/inward/record.url?scp=85086463005&partnerID=8YFLogxK

U2 - 10.1088/1757-899X/821/1/012038

DO - 10.1088/1757-899X/821/1/012038

M3 - Conference article

AN - SCOPUS:85086463005

SN - 1757-8981

VL - 821

JO - IOP Conference Series: Materials Science and Engineering

JF - IOP Conference Series: Materials Science and Engineering

IS - 1

M1 - 012038

T2 - 2019 3rd International Conference on Engineering and Applied Technology, ICEAT 2019

Y2 - 30 October 2019 through 1 November 2019

ER -