## On super H-Antimagicness of an Edge Comb Product of Graphs with Subgraph as a Terminal of its Amalgamation

##### Date

2018-02-28##### Author

DAFIK

AGUSTIN, Ika Hesti

NURVITANINGRUM, A.I

Prihandini, Rafiantika Megahnia

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Show full item record##### Abstract

All graphs in this paper are simple, nite, and undirected graph. Let r be a
edges of H. The edge comb product between L and H, denoted by LB
H, is a graph obtained
by taking one copy of L and jE(L)j copies of H and grafting the i-th copy of H at the
edges r to the i-th edges of L, we call such a graph as an edge comb product of graph
with subgraph as a terminal of its amalgamation, denoted by G = KBAmal(H; L H; n).
The graph G is said to admits an (a; d)-H-antimagic total labeling if there exist a bijection
f : V (G) [ E(G) ! f1; 2; : : : ; jV (G)j + jE(G)jg such that for all subgraphs isomorphic
to H, the total H-weights W(H) =
P
v2V (H)
f(v) +
P
f(e) form an arithmetic
sequence fa; a + d; a + 2d; :::; a + (t 1)dg, where a and d are positive integers and t is
e2E(H)
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 will study the
super Hantimagicness of disjoint union of edge comb product of graphs with subgraph as a
terminal of its amalgamation.

##### Collections

- LSP-Jurnal Ilmiah Dosen [7282]

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