Vol 4, No 3 (2016): CAUCHY

On The Local Metric Dimension of Line Graph of Special Graph

Marsidi, Marsidi (Unknown)
Dafik, Dafik (Unknown)
Hesti Agustin, Ika (Unknown)
Alfarisi, Ridho (Unknown)

Article Info

Publish Date
30 Nov 2016


Let G be a simple, nontrivial, and connected graph.  is a representation of an ordered set of k distinct vertices in a nontrivial connected graph G. The metric code of a vertex v, where , the ordered  of k-vector is representations of v with respect to W, where  is the distance between the vertices v and wi for 1≤ i ≤k.  Furthermore, the set W is called a local resolving set of G if  for every pair u,v of adjacent vertices of G. The local metric dimension ldim(G) is minimum cardinality of W. The local metric dimension exists for every nontrivial connected graph G. In this paper, we study the local metric dimension of line graph of special graphs , namely path, cycle, generalized star, and wheel. The line graph L(G) of a graph G has a vertex for each edge of G, and two vertices in L(G) are adjacent if and only if the corresponding edges in G have a vertex in common.

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Journal Info







Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...