ALFIYAH, SITI
(2013)
*EKSENTRIK DIGRAF DARI GRAF PLATONIK DAN GRAF RODA.*
Other thesis, University of Muhammadiyah Malang.

## Abstract

One of the applications of graph theory in mathematics that determined the shortest path from one city to another that consists of several routes, or path from one city to another of an area. This problem is equal to determine the eccentricity of a vertex on the graph. Eccentricity vertex n is denoted by e(n) of a vertex n connected graph G is defined as the maximum distance (maximum shortest path) from vertex n to another vertex on the graph G, so that the eccentricity of the vertex n can be written e (n) = max {d (n,i) | i V (G)}. Vertex i is called eccentric vertex of n if the distance from n to i equal to the eccentricity of n or e (n)= d (i,n) with i ∈ V (G). Eccentric digraph is denoted as ED (G) that a graph has the same set of vertex with a set of vertex in G or V (ED (G)) = V (G) and there will be an arc mn in ED (G) if m is an eccentric vertex of n. The purpose of the research is to get the general shape eccentric digraphs of platonic graph and wheel graph also characteristics eccentric digraph the platonic graph and wheel graph. The result of research are. (1). Eccentric digraph of platonic graph (other than tetrahedron graph) is a digraph ED (P) = (E,V) with E(ED(P))={(v_1 v_2 ) ⃡,(v_3 v_4 ) ⃡,Â…,(v_(n-1 ) v_n ) ⃡ } where n is the number of vertex on the platonic graph and V(ED(P))=V(P). Platonic graph have characteristic, to any vertex on platonic graph only one vertex has largest distance value (2). eccentric digraph of wheel graph W_n, n>3, eccentric digraphs of digraph ED(W_n ) with a set of vertex that V(ED(W_n ))={v_0,v_1,v_2,Â…,v_n } and the set of edges ie E(ED(W_n ))={(v_0 v_1 ) ⃗,(v_0 v_2 ) ⃗,Â…,(v_0 v_n ) ⃗ }∪{(v_i v_j ) ⃡ | i,j=1,2,Â…,n ;i≠j ;|i-j|≠1 ;|i-j|≠n-1} which is as a digraph (S_n ) ⃗∪((C_n ) ⃡ )^cand characteristics the wheel graph is the eccentricity central vertex (v_0) is 1, the eccentricity wheel vertex (v_i ) is 2, the eccentric vertex from central vertex (v_0) is wheel vertex (v_i ) and the eccentric vertex from wheel vertex (v_i ) is a vertex that is not adjacent with that vertex or not it is neighbors.

Item Type: | Thesis (Other) |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Teacher Training and Education > Department of Mathematics Education |

Depositing User: | Gusti Vani Putri Cahya |

Date Deposited: | 06 Feb 2015 06:17 |

Last Modified: | 06 Feb 2015 06:17 |

URI : | http://eprints.umm.ac.id/id/eprint/15776 |

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