- Tytuł:
- On Super $(a, d)$-$H$-Antimagic Total Covering of Star Related Graphs
- Autorzy:
-
Kathiresan, K.M.
Laurence, S. David - Powiązania:
- https://bibliotekanauki.pl/articles/31234087.pdf
- Data publikacji:
- 2015-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
super (a
d)-H-antimagic total labeling
star - Opis:
- Let $G = (V (G), E (G))$ be a simple graph and $H$ be a subgraph of $G$. $G$ admits an $H$-covering, if every edge in $E(G)$ belongs to at least one subgraph of $G$ that is isomorphic to $H$. An $(a, d)$-$H$-antimagic total labeling of $G$ is a bijection $ \lambda : V (G) \cup E(G) \rightarrow {1, 2, 3, . . ., |V (G)| + |E(G)|}$ such that for all subgraphs $ H^' $ isomorphic to $H$, the $H^′$ weights $ wt(H^') = \sum_{v \in V (H^') } \lambda (v) + \sum_{e \in E(H^')} \lambda (e) $ constitute an arithmetic progression $a$, $a+d$, $a+2d$, . . ., $a+(n−1)d$ where $a$ and $d$ are positive integers and $n$ is the number of subgraphs of $G$ isomorphic to $H$. Additionally, the labeling $ \lambda $ is called a super $(a, d)$-$H$-antimagic total labeling if $ \lambda (V (G)) = {1, 2, 3, . . ., |V (G)|} $. In this paper we study super $(a, d)-H$-antimagic total labelings of star related graphs $ G_u[S_n]$ and caterpillars.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 755-764
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł