Journal of Mathematics and Mathematics Education ISSN: 2089-8878 Vol.8, No.1, hal 20-30 Juli 2018 https://jurnal.uns.ac.id/jmme 20 DEKOMPOSISI GRAF MATAHARI (  ⨀         ) Putri Rizqi Musthofa 1 , Yemi Kuswardi 2 1,2 Prodi Pendidikan Matematika, FKIP, UNS Abstract:Graph theory is a branch of mathematics that facilitates problem solving. There are a lot of researches which concern on this issue. Various kinds of terms are introduced, one of them is graph decomposition. Graph decomposition is sub graphs collection of non-empty G graph {Hi} until Hi = 〈Ei〉 for non-empty sub graph Ei of E (G), where {Ei} is a partition of E (G). Sub graph Hi in decomposition G do not contain of isolated points. If {Hi} is a decomposition of G, it is denoted by  =         …    .The discussion of graph decomposition can be developed in graph decomposition through various types. One of the types is decomposition of sun graphs. Sun graph is a graph formed from a circle Cn in which each vertex on a circle graph is given one additional vertex with a degree. So, each vertex in sun graph has 3 degrees, except the edge of cortex which only have 1 degree. The sun graph is the result of corona between two graphs, namely a circular graph with n vertex and complement of a complete graph with 1 number of vertex (      ). The sun graph is denoted by   ⨀      where n is the number of vertex in circle graph. If the vertex naming refers to one vertex (with clockwise rules) and additional vertex naming connected to a circle vertex graph (vi), where the additional vertex has a degree of one, then the rule of naming is  + and sun graph is partitioned into a sub graph H_i = 〈Ei 〉 in the form of K 2 where i ≠ j so that H_i∩H_j = ∅, for i = 1,2,3, ..., n with sub graph   =   ,  + ,  + ,  + . If every i + 1, i + 2> n has an implicit + 1 and i + 2 will be expressed as an integers 1,2,3, ..., n (mod n), then the sun graph is 2K 2- decomposition. So, for sun graph   ⨀      n ≥3 is 2K2-decomposition. Keywords:Decomposition, Sun Graph. PENDAHULUAN Teori graf merupakan salah satu cabang ilmu matematika yang banyak digunakan untuk mempermudah suatu penyelesaian masalah. Teori graf merupakan pokok bahasan yang muncul pertama kali pada tahun 1736, yakni ketika Leonhard Euler mencoba untuk mencari solusi dari permasalahan yang sangat terkenal yaitu Jembatan Konigsberg. Teori ini sudah mengalami berbagai pengembangan baik dari sisi teori maupun terapannya. Beberapa masalah dalam dunia nyata dapat diselesaikan menggunakan konsep-konsep dalam teori graf, misal masalah jaringan di bidang ilmu komputer, riset operasi, komunikasi, dan ilmu-ilmu sosial atau ilmu pengetahuan alam (Chartrand (1977), Deo (1980)). Pada teori graf, kita mengenal bahwa sebuah graf G dinyatakan sebagai pasangan terurut dua himpunan, yaitu himpunan hingga tak kosong V(G) yang elemen – elemennya disebut titik dan himpunan berhingga yang mungkin kosong () yang elemen – elemennya disebut sisi sedemikian hingga setiap elemen dalam () merupakan pasangan tak berurutan dari titik – titik di (). () disebut himpunan titik dari graf G dan () disebut himpunan sisi dari graf  (Suryanto, 1986). Dalam teori ini, ada beberapa bentuk