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All Journal Jurnal Ilmu Dasar CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of Mathematical and Fundamental Sciences Contemporary Mathematics and Applications (ConMathA)

Liliek Susilowati

Department Of Mathematics, Faculty Of Sciences And Technology, Airlangga University, Jl. Mulyorejo, Surabaya 60115

Author-ID : 3399161

Astronomy Chemistry Control & Systems Engineering Earth & Planetary Sciences Materials Science & Nanotechnology Mathematics Physics

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Title

DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB Fryda Arum Pratama; Liliek Susilowati; Moh. Imam Utoyo
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 1 (2019)
Publisher : Universitas Airlangga

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm).

Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian Nurma Ariska Sutardji; Liliek Susilowati; Utami Dyah Purwati
Contemporary Mathematics and Applications (ConMathA) Vol. 1 No. 2 (2019)
Publisher : Universitas Airlangga

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

Hubungan Dimensi Metrik Ketetanggaan dan Dimensi Metrik Ketetanggan Lokal Graf Hasil Operasi Kali Korona Virdina Rahmayanti; Moh. Imam Utoyo; Liliek Susilowati
Contemporary Mathematics and Applications (ConMathA) Vol. 2 No. 1 (2020)
Publisher : Universitas Airlangga

Adjacency metric dimension and local adjacency metric dimension are the development of metric dimension. The purpose of this research is to determine the adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA(G⊙H), to determine the local adjacency metric dimension of corona graph between any connected graph G and non-trivial graph H denoted by dimA,l(G⊙H), and to determine the correlation between adjacency metric dimension and local adjacency metric dimension of corona product graph operations. In this research, it is found out that the value of adjacency metric dimension of G⊙H graph is affected by the basic characteristic of H and the domination characteristic. Meanwhile, the value of local adjacency metric dimension of G⊙H graph is only affected by the basic characteristic of H Futhermore, it is found a correlation of adjacency metric dimension and local adjacency metric dimension of corona product graph between any connected graph G and non-trivial graph H.

Co-Authors D. Dafik Dafik Dafik Fryda Arum Pratama Hendy Hendy M. Venkatachalam Moh. Imam Utoyo Moh. Imam Utoyo Mohammad Imam Utoyo Nurma Ariska Sutardji Prabhu, Savari Reni Umilasari S Slamin S Slamin Savari Prabhu Septory, Brian Juned Umilasari, Reni Utami Dyah Purwati Venkatachalam, M. Virdina Rahmayanti Yayuk Wayuni

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