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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

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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

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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<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

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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

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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

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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 in  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 v’ for each vertex v of a graph G , a new vertex v’ 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

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Abstract

ABSTRAK. Diberikan pemetaan bijektif f dari himpunan titik V(G) ke {1,2,…,|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

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Abstract

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

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Abstract

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

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Abstract

Graf  adalah graf dengan himpunan titik  dan himpunan sisi  dengan  sisi. Pelabelan graceful sisi-ganjil adalah pemetaan bijektif  yang mengakibatkan pemetaan  yang didefinisikan    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  graf Web .Keywords : graceful, graf graceful sisi-ganjil,  pelabelan graceful  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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (981.812 KB) | DOI: 10.14710/jfma.v1i1.4

Abstract

Abstract. This paper is addressed to discuss the edge super trimagic total labeling on some graphs which are corona, double ladder, quadrilateral snake and alternate triangular snake. The main results are the edge super trimagic total label for these graphs. Furthermore, it was prove that corona is a graph with edge super trimagic total labeling, a double ladder with odd ladder is graph with edge super trimagic total labeling, quadrilateral snake is a graph with edge super trimagic total labeling and finally an alternate triangular snake with odd ladder is graph with edge super trimagic total labeling. Abstrak. Dalam artikel ini, dibahas pelabelan total trimagic sisi untuk beberapa graf yaitu graf korona, graf double ladder, graf quadrilateral snake dan graf alternate triangular snake. Hasil utama dalam artikel ini adalah hasil-hasil pelabelan total trimagic sisi untuk graf-graf tersebut. Lebih lanjut, telah dibuktikan bahwa graf korona merupakan graf dengan pelabelan total trimagic sisi, graf double ladder dengan banyak ladder genap merupakan graf dengan pelabelan total trimagic sisi, graf quadrilateral snake merupakan graf dengan pelabelan total trimagic sisi, dan terakhir, graf alternate triangular snake merupakan graf pelabelan total trimagic sisi untuk banyak triangular genap.