On $H$-antimagicness of Cartesian product of graphs

Authors

MARTIN BACA
ANDREA SEMANICOVA-FENOVCIKOVA
MUHAMMAD AWAIS UMAR
DES WELYYANTI

DOI

10.3906/mat-1704-86

Abstract

A graph $G=(V(G),E(G))$ admits an $H$-covering if every edge in $E$ belongs to a~subgraph of $G$ isomorphic to $H$. A graph $G$ admitting an $H$-covering is called {\it $(a,d)$-$H$-antimagic} if there is a bijection $f:V(G)\cup E(G) \to \{1,2,\dots, V(G) + E(G) \}$ such that, for all subgraphs $H'$ of $G$ isomorphic to $H$, the $H$-weights, $wt_f(H')= \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e),$ constitute an arithmetic progression with the initial term $a$ and the common difference $d$. In this paper we provide some sufficient conditions for the Cartesian product of graphs to be $H$-antimagic. We use partitions subsets of integers for describing desired $H$-antimagic labelings.

Keywords

$H$-covering, super $(a, d)$-$H$-antimagic graph, partition of set, Cartesian product

First Page

339

Last Page

348

Recommended Citation

BACA, MARTIN; SEMANICOVA-FENOVCIKOVA, ANDREA; UMAR, MUHAMMAD AWAIS; and WELYYANTI, DES (2018) "On $H$-antimagicness of Cartesian product of graphs," Turkish Journal of Mathematics: Vol. 42: No. 1, Article 28. https://doi.org/10.3906/mat-1704-86
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/28