TY - JOUR
AU - Nanda, Ananda Dwi Nabila
AU - Hasmawati, Hasmawati
AU - Nur, Muh.
PY - 2023/09/06
Y2 - 2024/09/09
TI - Partition Dimention of Amalgamation-Side in Cycle Graph
JF - Jurnal Matematika, Statistika dan Komputasi
JA - JMSK
VL - 20
IS - 1
SE -
DO - 10.20956/j.v20i1.26808
UR - https://journal.unhas.ac.id/index.php/jmsk/article/view/26808
SP - 65-74
AB - <p><em>The graph </em> <em> is a pair of sets </em> <em>, where </em> <em> is a finite set whose elements are called vertices, and </em> <em> is the set of pairs of members of </em> <em>. which is called the edge. Let </em> <em> be a simple graph where </em> <em>. The distance between points </em> <em> and </em> <em> is denoted by </em> <em> is the length of the shortest path between </em> <em> and </em> <em>. Given </em> <em> and there is a vertex </em> <em> on the connected graph </em> <em>, then the distance between </em> <em> and </em> <em> is denoted</em> . If <em> is </em> <em>-partition of </em> <em>, then the representation of </em> <em> with respect to is </em> <em>-ordered pairs, </em> . <em>If the </em> <em>-ordered pairs </em> <em> for </em> <em> are all different, then the partition is called a dimension partition. The minimal </em> <em>-number which is the </em> <em>-differentiating partition of </em> <em> is called the partition dimension of </em> <em> and is denoted by </em> <em>. In this study, the partition dimensions of the sided amalgamation result will be determined on an even-order cycle graph. In determining the dimensions of the partition, characterization of the partition dimensions is used in the path graph, the lemma about the distinguishing set and the equivalence point, especially in the even-order cycle graph. The results of this study are</em> pd(Amal(Cn,e,k)) = 3 <em>for n≥4</em> , pd(Amal(C4,e,k))=4 <em>for</em> k=4 , pd(Amal(C4,e,k))=3+m for k=2m+3 and k=2m+4 where m=1,2,3,...</p>
ER -