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PELABELAN GRACEFUL SISI-GANJIL PADA GRAF WEB W(2,N) Rizky, Putri Dentya; Ratnasari, Lucia; ., Djuwandi
MATEMATIKA Vol 17, No 1 (2014): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Let G = (V(G),E(?)) be a graph with vertex set ?(?) and edge set ?(?). Assume that graph G have ? edge. Graceful edge-odd labeling is a bijective map  ? ? ?(?) ?  {1, 3, 5,?,2? ? 1} that resulting map ?+ : ?(?) ? {0,1,2,?,2? ?1} with  such as obtained different edge label. Graph G ia called Graceful edge-odd labeling if there is graceful edge-odd labeling on G. Let  and  are two cycle graph with vertex set  and . Graph  is obtained by conected every vertex from  to   such as we have edge  Graph Web W(2,n) is a graph obtained by adding a pendant edge on each outer cycle vertex from graph . In this paper we will discussed about Graceful edge-odd labeling on Web (2,?) graph and we have that Web W(2,?) graph is graceful edge odd graph for n odd.
PELABELAN E-CORDIAL PADA BEBERAPA GRAF CERMIN Suwarni, Ermi; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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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 V'1 and V'2 . The mirror graph is obtained by joining each vertex of vi?V2 to its corresponding vertex in v'i?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.
MENYELESAIKAN SISTEM PERSAMAAN LINIER MENGGUNAKAN ANALISIS SVD ahmad, irdam haidir; ratnasari, lucia
MATEMATIKA Vol 13, No 1 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Linear equation system, Ax = b, may be consistent or inconsistent. The approximate solution of  inconsistent of linear equation system can be determined. Gauss elimination or Gauss-Jordan elimination can be used to determine the solution of the consistent of linear equation system, but can?t for the inconsistent of linear equation system. Singular Value Decomposition (SVD) is matrix factorization method that closely associated with the singular value of the matrix. SVD analysis can be used to determined the orthonormal bases for the four fundamental subspaces associated with matrix A. That bases can be used to compute thesolution of the consistent and inconsistent of  linear equation system.  
PATH KUAT TERKUAT DAN JARAK KUAT TERKUAT DALAM GRAF FUZZY Ekawati, Lusia Dini; Ratnasari, Lucia
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Fuzzy graph is a graph consists pair of vertex and edge that have degree of membership containing closed interval of real number [0,1] on each node and edge. A graph fuzzy  is connected if the strength of connectedness between nodes u and v larger than zero for each . This paper will be explained about ss-path and ss-distance. Strongest stong path (ss-path) between two nodes in connected fuzzy graph if path is a strongest path as well as strong path. If G is a connected fuzzy graph then for each  there exists a strongest strong path for u to v . While ss-distane between two nodes u and v in connected fuzzy graph as the reciprocal of  the strength of connectedness between nodes u and v. Using metric can be known that every connected fuzzy graph is ss-selfcentered
PELABELAN CORDIAL UNTUK GRAF SPLIT DARI BEBERAPA GRAF Fitriana, Nisa Erma; Ratnasari, Lucia
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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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
METODE ASM PADA MASALAH TRANSPORTASI SEIMBANG Septiana, Arum Ryani; Solikhin, Solikhin; Ratnasari, Lucia
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

The transportation problem is special case on the linear programming which examines the goods? distribution for minimize shipping cost or maximize profits. In general, transportation problem requires two stages of completion, which is looking for feasible solution first and the look for the optimal solution. Abdul Quddoos, Dr. Shakeel Javaid, and Prof. Mohd Masood Khalid did some research for a new method, ASM method which is direct method with simple and fast way. This method relies on the cell that has the number 0 with the smallest index, and used to minimize transport costs. This final project determines the optimal solution using ASM method, both to mimize costs and maximize profits, and investigate the optimal method of ASM. The solution that obtained by ASM method on balanced transportation problem is always optimal, while for unbalanced transportation problem is not always optimal. The difference between algorithm for minimizing cases and maximize cases lies only in the first step, which is if the maximization case, then change c_ij into(-c_ij ).
SIFAT-SIFAT ISOMORFISMA GRAF FUZZY PADA GRAF FUZZY KUAT Handayani, Anik; Ratnasari, Lucia
MATEMATIKA Vol 15, No 1 (2012): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Fuzzy graph is a graph consists pairs of vertex and edge that have degree of membership containing closed interval of real number [0,1] on each edge and vertex. A fuzzy graph  is said to be a strong fuzzy graph if degree of membership edge with the same minimum degree of membership vertex and degree of membership vertex for each edge   with . In this paper describes the properties of fuzzy graphs isomorphism include weak isomorphism, co-weak isomorphism, and isomorphism on strong fuzzy graph.  
PELABELAN GRACEFUL GENAP BARU PADA GRAF CMPN Ratnasari, Lucia; Surarso, Bayu; Utomo, Robertus Heri Soelistyo
MATEMATIKA Vol 17, No 2 (2014): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Pelabelan Graceful pada graf dengan q sisi merupakan pemetaan injektif   , yang mengakibatkan pemetaan , yang didefinisikan dengan  bersifat bijektif. Graf yang memenuhi pelabelan graceful disebut graf graceful. T. Mahalaksmi Senthil Kumar, T. Abarna Parthiban dan T. Vanadhi [4], membuktikan graf CmÈPn merupakan graf graceful genap untuk m ganjil yang memenuhi kondisi tertentu. Marry U dan Saranya D [2], membuktikan bahwa graf CmÈPn merupakan graf graceful genap untuk m genap yang memenuhi kondisi tertentu. Pelabelan graceful genap didefinisikan sebagai pemetaan injektif  yang mengakibatkan pemetaan , yang didefinisikan  bersifat bijektif.  Tetapi pada pembuktian [4] dan [2], syarat injektif dan bijektif fungsinya tidak terpenuhi. Artikel ini mendefinisikan kembali pelabelan graceful genap pada graf CmÈPn sehingga syarat injektif dan bijektif fungsinya terpenuhi.  
PELABELAN PRIME CORDIAL PADA BEBERAPA GRAF YANG TERKAIT DENGAN GRAF SIKEL Hapsari, Nindita Yuda; Utomo, Robertus Heri Soelistyo; Ratnasari, Lucia
MATEMATIKA Vol 18, No 1 (2015): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Prime cordial labeling of a graph  is a bijective mapping of the set vertex  to the set  where  is the number of vertex . The edge labeling induced the vertex labeling, which is obtained by finding the great common divisor (gcd) of the label of vertex which it?s adjacent. If gcd of the adjacent vertex label is 1 then the label of edge is 1, but if gcd of the adjacent vertex label value other than 1 then the label of edge is 0, and the absolute value of the difference between the number of edges labeled 0 and the number of edges labeled 1 is less than equal with 1. A graph admits prime cordial labeling is called prime cordial graph. In this paper, we study about edge duplication cycle graph  (except for ), vertex duplication cycle graph , path union union of cycle the graph  and friendship graph one point union of    copies of cycle .
OPERASI GABUNGAN, JOIN, KOMPOSISI DAN HASIL KALI KARTESIAN PADA GRAF FUZZY SERTA KOMPLEMENNYA Novia, Tina Anggitta; Ratnasari, Lucia
MATEMATIKA Vol 13, No 3 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

A fuzzy graphs  is a nonempty set together with a pair function  and satisfied  This paper described about some operations on fuzzy graphs such as union, join, compositions and cartesian product. Complement of union two fuzzy graphs is join of their complement, join complement of two fuzzy graphs is union their complement. Complement of composition two strong fuzzy graphs is composition of their complement, but complement of cartesian product two stong fuzzy graphs is need not cartesian product of their complement.