The Analogy of Serial Murder Case as A Semi-Hamilton Simple Graph

1. The Analogy of Serial Murder Case as A Semi-Hamilton Simple Graph By : Megawati (J1A106023)

2. REASONING OF PROBLEM The criminal action, especially serial murder, that is murder happened in several times by the same perpetrator in certain time interval between one case to other cases. The cases can be formated a kind of certain pattern by an investigator to trace perpetrator and badness motif. By correlating the cases which happened at everyone of murder victim, it facilitates investigator to compile the pattern becomes a simple graph, where relationship every case is murder motif actually.

3. PurposeThis writing purpose to know usefulness of graph in the serial murder case. ProblemConstrain This writing only studies how exploiting of graph in investigation of serial murder case.

4. INTRODUCTION • A graph is an ordered pairG = (V,E) comprising a setV = {v1, v2, …,vn} of vertices or nodes together with a set E = {e1,e2, .., en} of edges or lines. • Simple graph : graph that has no loops and no more than one edge between any two different vertices. • Hamilton path is a path which pass every vertex in graph for once. • Hamilton circuit is a circuit which pass every vertex in graph for once, except origin vertex (end vertex at the same time) which is passed by twice. • Graph that has Hamilton circuit is called Hamilton's graph, while it which only has Hamilton path is called as semi-Hamilton graph.

5. Serial Murder in Graph • Serial Murder can be categorized as massacre (mass murder). Someone can be called serial killer if he had done three or more murder in certain range of time. • Graph which is formed by serial murder cases will form a simple graph and forms Hamilton path (non Hamilton circuit).

6. RESULTS AND DISCUSSION Graph of Ordinary Serial Murder • An ordinary serial murder which is be simplest is murder with three victim, each of them was murdered with the same method and has individuality that is precisely. • For example, a murderer kills Mr. 1, then Mr. 2 and Mr. 3 with certain interval at every his case. If this case is made graf, we will find: This graph forms a simple graph as Hamilton path.

7. Graph of Serial Murder with One of many Cases • Example, if there are six murder cases in certain time spread in an area, so it can be formed vertices which representation every case, like:

8. If after it is performed by investigation, police finds interrelationship between first, fifth, and, sixth murders. Hence, the graph can be made as follows: If in the later days is found interrelationship farther between other cases to this serial murder, the edges of graph will be changed according to requirement.

9. The serial murder case that was did by Ryan (a serial killer from Jombang, East Java) to his eleven victim, can be made a graph as follows:

10. Graph of "Continues" Serial Murder • At case the happening "continuation" of serial murder, that is serial murder with identical characteristic and method with serial murder before all but different perpetrator, investigator might possibly see entirely as a same cases. For example, happened six murder cases with identical characteristic and method in an area at a particular specified period:

11. Further investigation finds that first case perpetrator only did murder in first, second, and fourth case, temporary there is an other perpetrator was doing third, fifth, and sixth case by imitating first perpetrator to change suspicion. Hence, investigator will act quickly by changing graph structure becomes:

12. CONCLUSION Though the formulation method of serial murder only formulates murder case in the form of graph, and doesn't include formulas at all, only includes graph theorem, but formulation method of serial murder case to the form of graph has given a new viewpoint to all investigator, viewpoint that facilitates them to see a case runs as a whole, and assists them for performing an investigation.

13. THANKS....