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

Robiatul Adawiyah; D Dafik; S Slamin

doi:10.19184/kdma.v6i1.1826

Robiatul Adawiyah
D Dafik
S Slamin

DOI: https://doi.org/10.19184/kdma.v6i1.1826

Abstract

Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f: V(G)E(G) {1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a,d)-edge-antimagic total properties of connected £_n,m by using deductive axiomatic and the pattern recognition method. The result shows that a connected Lampion graphs admit a super (a,d)-edge antimagic total labeling for d = 0,1,2 for n It can be concluded that the result of this research has covered all the feasible d.

Key Words: (a,d)-edge antimagic vertex labeling, super (a,d)-edge antimagic total labeling, Lampion Graph.

Author Biography

Robiatul Adawiyah

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

Robiatul Adawiyah[1], Dafik[2], Slamin[3]

Abstract. A G graph of order p and size q is called an (a,d)-edge antimagic total if there exist a bijection f: V(G)E(G) {1,2,…,p+q} such that the edge-weights, w(uv)=f(u)+f(v)+f(uv), uv E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a,d)-edge-antimagic total properties of connected £_n,m by using deductive axiomatic and the pattern recognition method. The result shows that a connected Lampion graphs admit a super (a,d)-edge antimagic total labeling for d = 0,1,2 for n It can be concluded that the result of this research has covered all the feasible d.

Key Words: (a,d)-edge antimagic vertex labeling, super (a,d)-edge antimagic total labeling, Lampion 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