CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS

### Dimensi Metrik Ketetanggaan Lokal pada Graf Hasil Operasi Korona G odot P_3 dan G odot S_4

Alfin Nabila Taufik (University of Jember)
Dafik Dafik (University of Jember)
Rafiantika Megahnia Prihandini (University of Jember)
Ridho Alfarisi (University of Jember)

Publish Date
28 Dec 2020

#### Abstract

There are variant of the metric dimensions in graph theory, one of them is a local adjacency metric dimension. Let $W\subset V(G)$ with $W=\{w_1,w_2,\dots,w_k\}$, the representation of the vertex $V\in V(G)$, $r_A(v|W)=(d_A(v,w_1),d_A(v,w_2),\dots,d_A(v,w_k))$ with $d_ {A} (v, w)$= $0$ if $v = w$, $d_ {A} (v, w)$=  $1$ if $v$ adjacent to $w$, and $d_ {A} (v, w)$ =$2$ if $v$ does not adjacent to $w$.  If every two adjacent vertices $v_1$, $v_2 \in V (G)$,  $r_ {A} (v_1 | W) \neq r_ {A} (v_2 | W)$, then $W$ is the minimum cardinality of the local adjacency metric dimension. The minimum cardinality of $W$ is called the local adjacency metric dimension number, denoted by $\dim_{(A, l)} (G)$.  In this paper, we have found the  local adjacency metric dimension of corona product of special graphs, namely the $L_n \odot {P_3}$ graph, $S_n \odot {P_3}$ graph, $C_n \odot {P_3}$ graph, $P_n \odot {S_4}$ graph, and the graph $L_n \odot {S_4}$.

Journal Info

Abbrev

cgant

Publisher

Subject

Computer Science & IT Other

Description

Subjects suitable for publication include, the following fields of: Degree Diameter Problem in Graph Theory Large Graphs in Computer Science Mathematical Computation of Graph Theory Graph Coloring in Atomic and Molecular Graph Labeling in Coding Theory and Cryptography Dimensions of graphs on ...