Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902733 | AKCE International Journal of Graphs and Combinatorics | 2018 | 5 Pages |
Abstract
Let H and G be finite simple graphs where every edge of G belongs to at least one subgraph that is isomorphic to H. An (a,d)-H-antimagic total labeling of a graph G is a bijection f:V(G)âªE(G)â{1,2,â¦,|V(G)|+|E(G)|} such that for all subgraphs Hâ² isomorphic to H, the H-weights, w(Hâ²)=âvâV(Hâ²)f(v)+âuvâE(Hâ²)f(uv) form an arithmetic progression {a,a+d,â¦,a+(kâ1)d} where a>0,dâ¥0 are two fixed integers and k is the number of subgraphs of G isomorphic to H. Moreover, if the vertex set V(G) receives the minimum possible labels {1,2,â¦,|V(G)|}, then f is called a super(a,d)-H-antimagic total labeling. In this paper we study super (a,d)-Cn-antimagic total labeling of a disconnected graph, namely mCn.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Faisal Susanto,