Super local edge anti-magic total coloring of paths and its derivation

Hadiputra, F. F.; Silaban, Denny Riama; Maryati, Tita Khalis

doi:10.19184/ijc.2019.3.2.6

Cited by 3 publications

(3 citation statements)

References 5 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…dan 𝐸(𝑢) adalah himpunan sisi yang berinsiden ke 𝑢 [2,3]. Jika pelabelan titik total anti-ajaib lokal melabeli sisi terlebih dahulu maka pelabelaan titik total super anti-ajaib lokal melabeli titik terlebih dahulu.…”

Section: Pendahuluanunclassified

PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

Setyawan

Afni

Prihandini

et al. 2021

BAREKENG: J. Il. Mat. & Ter.

View full text Add to dashboard Cite

The local antimagic total vertex labeling of graph G is a labeling that every vertices and edges label by natural number from 1 to such that every two adjacent vertices has different weights, where is The sum of a vertex label and the labels of all edges that incident to the vertex. If the labeling start the smallest label from the vertex then the edge so that kind of coloring is called the local super antimagic total vertex labeling. That local super antimagic total vertex labeling induces vertex coloring of graph G where for vertex v, the weight w(v) is the color of v. The minimum number of colors that obtained by coloring that induces by local super antimagic total vertex labeling of G called the chromatic number of local super antimagic total vertex coloring of G, denoted by χlsat(G). In this paper, we consider the chromatic number of local super antimagic total vertex coloring of Generalized Petersen Graph P(n,k) for k=1, 2.

show abstract

Section: Pendahuluanunclassified

PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

Setyawan

Afni

Prihandini

et al. 2021

BAREKENG: J. Il. Mat. & Ter.

View full text Add to dashboard Cite

show abstract

“…The super local antimagic chromatic number of some graphs have been discovered such as fan, gear, sunflower [10], star, double star, cycle, path, cubic bipartite, wheel, amalgamation of graph, and several joint product graphs [12]. On the other hand, the super edge local antimagic total chromatic number has been discovered for path and its derivation, hedge, hedgerow, star, and an amalgamation of graphs [5].…”

Section: Introductionmentioning

confidence: 99%

On local antimagic vertex coloring of corona products related to friendship and fan graph

Himami

Silaban

2021

IJC

Self Cite

View full text Add to dashboard Cite

Let G=(V,E) be connected graph. A bijection f : E → {1,2,3,..., |E|} is a local antimagic of G if any adjacent vertices u,v ∈ V satisfies w(u)≠ w(v), where w(u)=∑e∈E(u) f(e), E(u) is the set of edges incident to u. When vertex u is assigned the color w(u), we called it a local antimagic vertex coloring of G. A local antimagic chromatic number of G, denoted by χla(G), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of G. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on m vertices, namely, χla(Fn ⊙ \overline{K_m}) and χla(f(1,n) ⊙ \overline{K_m}).

show abstract

“…The study is followed by Rajkumar and Nalliah [15] who investigated the local edge antimagic chromatic number of friendship graphs F n , wheels W n , fan graphs f n , helm graph H n , and flower graphs F l n . Many variations on local antimagic labeling may also be seen in [5,8,9]. To see many other kinds of labeling please consult to [6].…”

mentioning

confidence: 99%

A note on local edge antimagic chromatic number of graphs

Hadiputra,

Maryati

2024

Proyecciones (Antofagasta)

View full text Add to dashboard Cite

Let $G$ be a finite, undirected and simple graph. A bijection $f : V(G) \to [1,|V(G)|]$ is called a local edge antimagic labeling if for any two adjacent edges $uv,vw \in E(G), f(u) \ne f(w)$. The local edge antimagic chromatic number $\ch(G)$ is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of $G$. In this paper, we investigate characterization of graphs $G$ with small number $\ch(G)$, relationship between local edge antimagic chromatic number $\ch(G)$ and edge independence number $\alpha'(G)$, and bounds of $\ch(G)$ for any graphs.

show abstract

Super local edge anti-magic total coloring of paths and its derivation

Cited by 3 publications

References 5 publications

PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

On local antimagic vertex coloring of corona products related to friendship and fan graph

A note on local edge antimagic chromatic number of graphs

Contact Info

Product

Resources

About