Lucia Ratnasari
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Published : 20 Documents
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Energi Derajat Maksimal pada Graf Terhubung Setyowidi, Destika Dwi; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : Jurnal Matematika

#### Abstract

Graf G adalah pasangan himpunan (V,E) , dengan V(G) adalah himpunan titik G dan E(G) adalah himpunan sisi G . Graf G dapat direpresentasikan ke dalam matriks derajat maksimal. Dari matriks derajat maksimal diperoleh polinomial karakteristik μn+c1μn-1+c2μn-2+…+cn dengan koefisien c1 merupakan traceM(G) , c2 merupakan penjumlahan dari determinan submatriks order 2, c3 merupakan penjumlahan dari determinan submatriks order 3. Energi derajat maksimal graf G adalah penjumlahan dari harga mutlak nilai eigen derajat maksimal. Energi derajat maksimal graf star (Sn+1) , graf sikel (Cn) , graf path Pn , dan graf regular r bernilai kurang dari energi derajat maksimal graf komplit (Kn) . Energi derajat maksimal EMG berupa bilangan rasional dengan bilangan rasional tersebut adalah bilangan bulat genap
PENYELESAIAN MASALAH LINTASAN TERPENDEK FUZZY DENGAN MENGGUNAKAN ALGORITMA CHUANG – KUNG DAN ALGORITMA FLOYD Musfiroh, Anik; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : Jurnal Matematika

#### Abstract

Abstract : In the classic graph, shortest path problem is related problem with determination of the which are connected in a graph that form the shortest distance between source node and the destination node. This idea is extended to solve the fuzzy shortest path problem. In this paper, will be discussed about Chuang - Kung algorithm and Floyd algorithm to solve shortest path problem. Chuang - Kung algorithm’s steps is to determine all pass possible path from source node to destination node, then compute value of similarity degree SLmin, Li with Lmin is the fuzzy shortest length and Li is length of possible path. While for Floyd algorithm, the first step is to determine the initial distance matrix D0 and the  matrix of the initial order S0 , then check this elements. If in matrix Dk element is dik+dkj&lt;dij so dij replaced with Lmin dij, dik+dkj . Then replace elements matrix Sk with k . Changes sij in matrix Sk following to changes dij on matrix Dk .
PRODUK GRAF FUZZY INTUITIONISTIC Ningrum, Zumiafia Ross Yana; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : Jurnal Matematika

#### Abstract

An intuitionistic fuzzy graph G:V,E consist of a couples of node sets V and set of edges E which the sum of degree membership and degree non membership each of nodes and each of edges in closed interval [0,1], the degree membership each of edges is less than or equal with the minimum of degree membership each nodes of incident, and degree non membership each of edges is less than or equal with the maximum degree non membership each nodes of incident. Product fuzzy graph was defined by Dr. V. Ramaswamy and Poornima B. Product fuzzy graph is fuzzy graph, where the degree membership each of edges is less than or equal with product of the between degree of membership each nodes of incident. In this paper we study the definitions of product intuitionistic fuzzy graph, product intuitionistic fuzzy graph complete, further discussion about the complement of product intuitionistic fuzzy graph, join of product intuitionistic fuzzy graph and multiplication of product intuitionistic fuzzy graph and their characteristics.
PELABELAN E-CORDIAL PADA BEBERAPA GRAF CERMIN Suwarni, Ermi; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : Jurnal Matematika

#### Abstract

Abstract: Let G be a graph with vertex set V(G) and edge set E(G) . Difine on function f of E(G) to {0,1}, for v∈V(G) value f(v) is obtained by two modulo price of amount of edges label than have insident to the vertex v . The function f is called an E -cordial labeling of G if conditions absolute value from difference the number of vertexs having label 0 and the number having label 1 less or equal 1, and absolute value from difference the number of edges having label 0 and the number of edges having label 1 less or equal 1. Graph which admits of E -cordial labeling is E-cordial graph. The mirror graph M(G) is a bipartite graph with a partite sets V1 and V2 and G be the copy of G with corresponding partite sets V1 and V2 . The mirror graph is obtained by joining each vertex of vi∈V2 to its corresponding vertex in vi∈V2 by an edge. In this paper we study about labeling of mirror graph for cycle graph, path graph, hypercube graph and bipartite complite graph. The mirror graph of cycle graph, path graph, hypercube graph, and bipartite complite graph are E-cordial graphs.
PELABELAN CORDIAL UNTUK GRAF SPLIT DARI BEBERAPA GRAF Fitriana, Nisa Erma; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : Jurnal Matematika

#### Abstract

Cordial labeling is a binary point labeling that have absolute value condition of the difference in the number of vertices having label 0 and the number of vertices having label 1 is less than or equal to 1 dan absolute value of the difference inÂ  the number of edges having label 0 and the number of edges having label 1 is less than or equal to 1. Graph which qualified of cordial labeling is called cordial graph. Split graph S(G) is the graph obtained by taking a new vertex vâ for each vertex v of a graph G , a new vertex vâ is connected to all vertices of G which adjacent to v . In this final paper explored about cordial labeling for split graph of path graph, cycle graph, wheel graph, matching graph, fan graph, bipartite complete graph, and k copies star graph
PELABELAN DIVISOR CORDIAL PADA BEBERAPA GRAF Wijayanti, Aptri; Ratnasari, Lucia
Jurnal Matematika Vol 2, No 3 (2013): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

#### Abstract

ABSTRAK. Diberikan pemetaan bijektif f dari himpunan titik V(G) ke {1,2,â¦,|V|}. Pelabelan sisi induced berlabel 1 apabila f(u) dapat membagi f(v) atau f(v) dapat membagi f(u) dan berlabel 0 untuk yang lainnya, dimana u dan v adalah titik yang incident dengan sisi uv. Pemetaan f disebut pelabelan divisor cordial bila harga mutlak dari selisih banyaknya sisi yang mempunyai label 0 dan banyaknya sisi yang mempunyai label 1 kurang dari atau sama dengan 1. Graf yang memenuhi syarat pelabelan divisor cordial disebut graf divisor cordial. Pada jurnal ini dikaji bahwa graf path, graf cycle, graf wheel, graf star, graf bipartit lengkap K_(2,n), graf bistar dan graf subdivisi dari graf star (S(K_(1,n) )) merupakan graf divisor cordial.
PELABELAN GRACEFUL SATU MODULO PADA BEBERAPA GRAF EULE Isa, Isa; Ratnasari, Lucia
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

#### Abstract

Â ABSTRACT. A graph Â with Â edges is said to be one modulo Â graceful graph () if there is a injective function from vertex set of graph Â to Â in such a way that Â induces a function Â from edge set of graph Â to Â defined as Â is bijective.Â  In this Last Project, the following Euler graphs : n-polygonal snakes, Â and Â under certain conditions which admit one modulo Â graceful labeling () are learned.Â Â
PELABELAN GRACEFUL SATU MODULO PADA BEBERAPA GRAF EULE Isa, Isa; Ratnasari, Lucia
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

#### Abstract

Â ABSTRACT. A graph Â with Â edges is said to be one modulo Â graceful graph () if there is a injective function from vertex set of graph Â to Â in such a way that Â induces a function Â from edge set of graph Â to Â defined as Â is bijective.Â  In this Last Project, the following Euler graphs : n-polygonal snakes, Â and Â under certain conditions which admit one modulo Â graceful labeling () are learned.Â Â
PELABELAN GRACEFUL SISI-GANJIL PADA BEBERAPA GRAF Dentya Rizky, Putri; Ratnasari, Lucia
Jurnal Matematika Vol 3, No 3 (2014): JURNAL MATEMATIKA
Publisher : Jurnal Matematika

#### Abstract

Graf Â adalah graf dengan himpunan titik Â dan himpunan sisi Â dengan Â sisi. Pelabelan graceful sisi-ganjil adalah pemetaan bijektif Â yang mengakibatkan pemetaan Â yang didefinisikan Â  Â sehingga diperoleh label titik berbeda. Graf G dikatakan graf graceful sisi-ganjil jika terdapat pelabelan graceful sisi-ganjil pada graf G. Pada Tugas Akhir ini dikaji tentang pelabelan graceful sisi-ganjil pada graf , graf Double Star , graf , graf Roda . Selanjutnya pada Tugas Akhir ini diberikan konstruksi pelabelan graceful sisi-ganjil pada graf Helms , graf Â graf Web .Keywords : graceful, graf graceful sisi-ganjil, Â pelabelan graceful Â sisi-ganjil
PELABELAN TOTAL SUPER TRIMAGIC SISI PADA BEBERAPA GRAF Utomo, R. Heri Soelistyo; Tjahjana, Heru; Irawanto, Bambang; Ratnasari, Lucia
Journal of Fundamental Mathematics and Applications (JFMA) Vol 1, No 1 (2018): Journal of Fundamental Mathematics and Applications
Publisher : Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University