Pelabelan Total Super $(a,d)$-sisi Antimagic pada Gabungan Saling Lepas Graf Bintang dengan Teknik Pewarnaan Titik

Abstract

For a graph $G=(V,E)$, a bijection $f$ from $V(G) \cup E(G)$ into $\{1, 2,3,\ldots,$ $|V(G)|+|E(G)|\}$ is called ($a$,$d$)-edge-antimagic total  labeling of $G$ if the edge-weights $w(xy) = g(x) + g(y) + g(xy), xy \in E(G)$, form an arithmetic progression starting from $a$ and having common difference $d$. An ($a$,$d$)-edge-antimagic total labeling is called super ($a$,$d$)-edge-antimagic total labeling if $g(V(G))= \{1, 2,\ldots,|V(G)|\}$. A vertex coloring is an assignment of labels or colors to each vertex of a graph such that there is no two adjacent vertices have the same colors. We can use vertex coloring technique to label the vertices of a graph such that it has EAV-weight. Furthermore, If we have an EAV-weight of $S_n$, we can construct a super $(a,d)$-edge antimagic total labeling of Star Graph, either simple or disjoint union of this graph.