1 results
ON
$H$-ANTIMAGICNESS OF DISCONNECTED GRAPHS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
- Published online by Cambridge University Press:
- 01 April 2016, pp. 201-207
- Print publication:
- October 2016
-
- Article
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- You have access
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A simple graph
$G=(V,E)$ admits an 
$H$-covering if every edge in 
$E$ belongs to at least one subgraph of 
$G$ isomorphic to a given graph 
$H$. Then the graph 
$G$ is 
$(a,d)$-
$H$-antimagic if there exists a bijection 
$f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs 
$H^{\prime }$ of 
$G$ isomorphic to 
$H$, the 
$H^{\prime }$-weights, 
$wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$, form an arithmetic progression with the initial term 
$a$ and the common difference 
$d$. When 
$f(V)=\{1,2,\ldots ,|V|\}$, then 
$G$ is said to be super 
$(a,d)$-
$H$-antimagic. In this paper, we study super 
$(a,d)$-
$H$-antimagic labellings of a disjoint union of graphs for 
$d=|E(H)|-|V(H)|$.
