Super $(a,d)$-$\mathcal{H}$-Antimagic Total Covering of Amalgamation Graph $K_4$ and $W_4$

  • Novri Anggraeni
  • Dafik Dafik

Abstract

A graph $G(V,E)$ has a $\mathcal{H}$-covering if every edge in $E$ belongs to a subgraph of $G$ isomorphic to $\mathcal{H}$. An $(a,d)$-$\mathcal{H}$-antimagic total covering is a total labeling $\lambda$ from $V(G)\cup E(G)$ onto the integers $\{1,2,3,...,|V(G)\cup E(G)|\}$ with the property that, for every subgraph $A$ of $G$ isomorphic to $\mathcal{H}$ the $\sum{A}=\sum_{v\in{V(A)}}\lambda{(v)}+\sum_{e\in{E(A)}}\lambda{(e)}$ forms an arithmetic sequence. A graph that admits such a labeling is called an $(a,d)$-$\mathcal{H}$-antimagic total covering. In addition, if $\{\lambda{(v)}\}_{v\in{V}}=\{1,...,|V|\}$, then the graph is called $\mathcal{H}$-super antimagic graph. In this paper we study of amalgamasi graph $K_4$ and $W_4$.
Published
2014-11-19
How to Cite
ANGGRAENI, Novri; DAFIK, Dafik. Super $(a,d)$-$\mathcal{H}$-Antimagic Total Covering of Amalgamation Graph $K_4$ and $W_4$. Prosiding Seminar Matematika dan Pendidikan Matematik, [S.l.], v. 1, n. 1, nov. 2014. Available at: <https://jurnal.unej.ac.id/index.php/psmp/article/view/926>. Date accessed: 05 june 2020.
Section
Prosiding Seminar Nasional Matematika 2014