| dc.description.abstract | Let Hi be a finite collection of simple, nontrivial and undirected graphs and let each Hi
have a fixed vertex vj called a terminal. The amalgamation Hi as vj as a terminal is formed
by taking all the Hi’s and identifying their terminal. When Hi are all isomorphic graphs,
for any positif integer n, we denote such amalgamation by G = Amal(H, v, n), where n
denotes the number of copies of H. The graph G is said to be an (a, d)-H-antimagic total
graph if there exist a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|}
such that for all subgraphs isomorphic to H, the total H-weights w(H) = P
v∈V (H)
P
f(v)+
e∈E(H)
f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (t − 1)d}, where a
and d are positive integers and t is the number of all subgraphs isomorphic to H. An (a, d)-
H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In
this paper, we study a super (a, d)-H antimagic total labeling of G = Amal(H, v, n) and
its disjoint union when H is a complete graph. | en_US |
