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All Journal Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding JTAM (Jurnal Teori dan Aplikasi Matematika) InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS JPMA Emerging Statistics and Data Science Journal
Kusbudiono Kusbudiono, Kusbudiono
Jurusan Matematika FMIPA Universitas Jember
Humanities Computer Science & IT Education Environmental Science Mathematics Other

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Journal : unej e-proceeding

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On The Metric Dimension with Non-isolated Resolving Number of Some Exponential Graph S. M. Yunika; Slamin Slamin; Dafik Dafik; Kusbudiono Kusbudiono
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Let w, w ∈ G = (V, E). A distance in a simple, undirected and connected graph G, denoted by d(v, w), is the length of the shortest path between v and w in G. For an ordered set W = {w1, w2, w3, . . . , wk} of vertices and a vertex v ∈ G, the ordered k-vector r(v|W) = (d(v, w1), d(v, w2), . . . , d(v, wk)) is representations of v with respect to W. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The metric dimension dim(G) of G is the minimum cardinality of resolving set for G. The resolving set W of graph G is called non-isolated resolving set if subgraph W is induced by non-isolated vertex. While the minimum cardinality of non-isolated resolving set in graph is called a non-isolated resolving number, denoted by nr(G). In this paper we study a metric dimension with non-isolated resolving number of some exponential graph.
On Total r-Dynamic Coloring of Several Classes of Graphs and Their Related Operations Kusbudiono Kusbudiono; Desi Febriani Putri; Dafik Dafik; Arika Indah Kristiana
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

All graphs in this paper are simple, connected and undirected. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. A total r-dynamic coloring is a proper k-coloring c of G, such that ∀v ∈ V (G), |c(N(v))| ≥ min[r, d(v) + |N(v)|] and ∀uv ∈ E(G), |c(N(uv))| ≥ min[r, d(u) + d(v)]. The total r-dynamic chromatic number, written as χ ′′r (G), is the minimum k such that G has an r-dynamic k-coloring. Finding the total r-dynamic chromatic number is considered to be a NP-Hard problems for any graph. Thus, in this paper, we initiate to study χ′′ r (G) of several classes of graphs and and their related operations.
On the Rainbow Vertex Connection Number of Edge Comb of Some Graph Agustina M.; Dafik Dafik; Slamin Slamin; Kusbudiono Kusbudiono
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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By an edge comb, we mean a graph formed by combining two graphs G and H, where each edge of graph G is replaced by the which one edge of graph H, denote by G D H. A vertex colored graph G D H = (V (G D H);E(G D H)) is said rainbow vertex-connected, if for every two vertices u and v in V (G D H), there is a u ???? v path with all internal vertices have distinct color. The rainbow vertex connection number of G D H, denoted by rvc(G D H) is the smallest number of color needed in order to make G D H rainbow vertex-connected. This research aims to find an exact value of the rainbow vertex connection number of exponential graph, namely rvc(G D H) when G D H are Pn D Btm, Sn D Btm, Ln D Btm, Fm;n D Btp, rvc(Pn D Sm), rvc(Cn D Sm), and rvc(Wn D Sm) Wn D Btm. The result shows that the resulting rainbow vertex connection attain the given lower bound.
DESAIN JARINGAN INTERNET INDIHOME DI PERUMAHAN MANGGAR PERMAI AMBULU MENGGUNAKAN ALGORITMA K-MEANS DAN KRUSKAL Reggy Valentinnes Septa Jeniusa; Kiswara Agung Santoso; Kusbudiono Kusbudiono
UNEJ e-Proceeding 2022: E-Prosiding Seminar Nasional Matematika, Geometri, Statistika, dan Komputasi (SeNa-MaGeStiK)
Publisher : UPT Penerbitan Universitas Jember

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Based on the survey results of the Association of Indonesian Internet Service Providers, internet users are increasing reaching 196.7 million people. This community need is the driving force for PT. Telkom to overcome the need for internet access, namely the presence of Indihome. The Indihome internet network is distributed to several houses through ODP. The grouping of houses on ODP is based on the closest distance using the k-means algorithm. Meanwhile, minimizing the use of Indihome internet cables using the Kruskal algorithm. The data used in this study are house coordinates data obtained from the Google Earth application. The data is processed using the k-means algorithm, then continued using the Kruskal algorithm. The results of the research are clustering in houses with ODP formed 16 clusters which are processed using the k-means algorithm and stop at the 5th iteration. The ODP used has capacities of 8 and 12. ODP 1, 2, 4, 5, 8, 9, 11, 12, 13, 14, 15, 16 have capacities of 8. While ODP 3, 6, 7, 10 has a capacity of 12. Fiber optic cable between ODP is processed using the Kruskal algorithm and produces a minimum weight of 0.006601782 or ± 735 meters. Keywords: Indihome, K-Means Algorithm, Kruskal Algorithm
Co-Authors Agustina M. Arika Indah Kristiana Aulia, Safira Nur Bagus Arief Setiawan D. Dafik Desi Febriani Putri Desi Febriani Putri Fahreza, Faizal Rifky Hadi Siswanto Hani'ah Zakin I Made Tirta Ida Ariska Ika Hesti Agustin, Ika Hesti Ikhsanul Halikin, Ikhsanul Juliyanto, Bagus Kiswara Agung Santoso Kosala Dwidja Purnomo Kristiana Wijaya Maya Ayu P, Maya Ayu Moh. Hasan Mustafa , Meiunike Indah NURIL AFANDI, NURIL Reggy Valentinnes Septa Jeniusa Reyka Bella Desvandai Riza Nurfadila Rusli Hidayat S Slamin S. M. Yunika Setiawan, Bagus Arief Titis Miranti, Titis Viqedina Rizky Noviyanti Wahyu Nikmatus Sholihah Wanda Olyvia Anggraini, Wanda Olyvia