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Yemi Kuswardi
Prodi Pendidikan Matematika, FKIP, UNS
Education Mathematics

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DEKOMPOSISI GRAF HELM Risti Dwi Rahayu; Yemi Kuswardi
Journal of Mathematics and Mathematics Education Vol 8, No 1 (2018): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v8i1.25822

Abstract

Abstract: Decomposition of graph G is a collection of {Hi} from sub graph G until Hi = 〈Ei〉 for Ei subset E (G) and {Ei} is partitions of E (G). If {Hi} is a decomposition of G, it can be written as the addition of the sides and G is decomposed into sub graphs where n = |{Hi}|. In other words, is the decomposition of graph G. Helm Hn graph with n ≥ 3 and n is even number which can be partitioned into sub graph   which is in the form of 2K2, where Hn = So, helmet Hn graph with n ≥ 3 and n is an even number of 2K2-decomposition. The Hn helm graph with n > 3 can be partitioned into sub graph Ai = 〈Ei〉 which is in the form of 3K2, where . So that the Hn helm graph with n > 3 is 3K2-decomposition.Keywords:Decomposition, Helm Graph.
DEKOMPOSISI GRAF MATAHARI Putri Rizqi Musthofa; Yemi Kuswardi
Journal of Mathematics and Mathematics Education Vol 8, No 1 (2018): Journal of Mathematics and Mathematics Education (JMME)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jmme.v8i1.25820

Abstract

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 K2 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 2K2-decomposition. So, for sun graph n ≥3 is 2K2-decomposition.Keywords:Decomposition, Sun Graph. 
Co-Authors Putri Rizqi Musthofa Risti Dwi Rahayu