Amalgamations and Cycle-Antimagicness

A finite simple graph
$G$
is called a
$(c,d)$
-
$H$
-antimagic if
$G$
satisfies the following properties: (i)
$G$
has an
$H$
-covering by the family of subgraphs
$H_{1},H_{2}, {\dots },H_{r}$
where every
$H_{t}\cong H, 1\leq t\leq r$
, (ii) there exists a bijection
$\beta: V\cup E \rightarrow \{1,2,3, {\dots },|V\cup E|\}$
such that the
$H$
-weights constitute an arithmetic progression with initial term
$c$
and common difference
$d$
, where
$c > 0, d \ge 0$
are integers. The labeling
$\beta $
is called super if smallest possible labels appear on vertices of graph
$G$
. For
$m \in \mathbb {N}$
and
$m \geq 2$
, let
$\{G_{i}\}_{i=1}^{m}$
be a collection of graphs with
$u_{i} \in V(G_{i})$
as a fixed vertex. The vertex amalgamation, denoted by
$Amal(G_{i}, \{u_{i}\}, m)$
, is a graph formed by taking all the
$G_{i}$
’s and identifying
$u_{i}$
’s. In this research article, we studied super
$(c,1)-C_{3}$
-antimagic labelings of amalgamation
$Amal(G_{i}, \{u_{i}\}, m)$
of wheels, fans and flower graphs.