# Super complete-antimagicness of Amalgamation of any Graph

**Journal**: International Journal of Advanced Engineering Research and Science (Vol.4, No. 5)

**Publication Date**: 2017-05-08

**Authors** : R.M Prihandini; Ika Hesti Agustin; Dafik; Ridho Alfarisi;

**Page** : 202-206

**Keywords** : Super H-antimagic total graph; Amalgamation of graph; arithmetic sequence.;

### Abstract

Let H_i be a finite collection of simple, nontrivial andundirected graphs and let each H_i have a fixed vertex v_jcalled a terminal. The amalgamation H_i as v_j as a terminal isformed by taking all the H_i's and identifying their terminal.When H_(i )are all isomorphic graphs, for any positif integer nwe denote such amalgamation by G=Amal(H,v,n), where ndenotes the number of copies of H. The graph G is said to be an(a,d)-H-antimagic total graph if there exist a bijectivefunction f: V(G)âˆª E(G)â†' {1,2,â€¦ ,|V (G)| +|E(G)|} such that for all subgraphs isomorphic to H, the totalH-weights W(H)=âˆ‘_(vâˆˆ V(H)) f(v)+âˆ‘_(eâˆˆ E(H)) f(e) forman arithmetic sequence {a,a + d,a +2d,...,a+(n - 1)d}, wherea and d are positive integers and n is the number of allsubgraphs isomorphic to H. An (a,d)-H-antimagic total labelingfis called super if the smallest labels appear in the vertices.In this paper, we study a super (a,d)-H antimagic totallabeling of G=Amal(H,v,n) and its disjoint union.

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Last modified: 2017-06-04 02:29:24