Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1704-86
Keywords
$H$-covering, super $(a, d)$-$H$-antimagic graph, partition of set, Cartesian product
First Page
339
Last Page
348
Recommended Citation
BACA, M, SEMANICOVA-FENOVCIKOVA, A, UMAR, M. A, & WELYYANTI, D (2018). On $H$-antimagicness of Cartesian product of graphs. Turkish Journal of Mathematics 42 (1): 339-348. https://doi.org/10.3906/mat-1704-86
