SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH

  • Dian Anita Hadi
  • D Dafik
  • S Slamin

Abstract

Abstract. An  (a, d)-edge-antimagic  total   labeling  of G  is a  one-to-one  mapping taking the vertices and edges onto {1, 2, 3, . . . , p + q} Such that the edge-weights w(uv)  = (u)+(v)+(uv), uv E(G)  form an arithmetic sequence {a, a+d, a+2d, . . . , a+ (q − 1)d}, where first term  a > 0 and  common  difference d ≥ 0.  Such a graph G is called super if the smallest possible labels appear on the vertices.  In this paper we will study a super edge-antimagic total labelings properties of connective Swn graph.   The result shows that a connected Silkworm graph admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all the feasible n, d.

 

Key Words: (a, d)-edge-antimagic total labeling, super (a, d)-edge-antimagic total labeling, Silkworm graph.


Author Biography

Dian Anita Hadi

SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH

 

Dian Anita Hadi[1], Dafik[2], Slamin[3]

Abstract. An  (a, d)-edge-antimagic  total   labeling  of G  is a  one-to-one  mapping taking the vertices and edges onto {1, 2, 3, . . . , p + q} Such that the edge-weights w(uv)  = (u)+(v)+(uv), uv E(G)  form an arithmetic sequence {a, a+d, a+2d, . . . , a+ (q − 1)d}, where first term  a > 0 and  common  difference d ≥ 0.  Such a graph G is called super if the smallest possible labels appear on the vertices.  In this paper we will study a super edge-antimagic total labelings properties of connective Swn graph.   The result shows that a connected Silkworm graph admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all the feasible n, d.

 

Key Words: (a, d)-edge-antimagic total labeling, super (a, d)-edge-antimagic total labeling, Silkworm graph.


[1] Student of Mathematics Education Department  Jember University

[2] Lecturer of Mathematics Education Department  Jember University

[3] Lecturer of Information System Department Jember University

Published
2015-04-01
How to Cite
HADI, Dian Anita; DAFIK, D; SLAMIN, S. SUPER (a,d)-EDGE-ANTIMAGIC TOTAL LABELING OF SILKWORM GRAPH. Kadikma, [S.l.], v. 6, n. 1, apr. 2015. ISSN 2686-3243. Available at: <https://jurnal.unej.ac.id/index.php/kadikma/article/view/1828>. Date accessed: 28 mar. 2024. doi: https://doi.org/10.19184/kdma.v6i1.1828.
Section
Articles