EXISTENCE OF CLOSED DISTANCE MAGIC GRAPHS FOR PARTICULAR MAGIC CONSTANTS
Let ???? = (????,????) be a finite, simple, and undirected graph with ???? vertices. A labeling ???? from the vertex set ???? to the set of ???? first natural numbers is called a distance magic labeling if there exists a constant ???? such that for every vertex ?????????, the sum of all its neighbo...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/42361 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let ???? = (????,????) be a finite, simple, and undirected graph with ???? vertices. A labeling
???? from the vertex set ???? to the set of ???? first natural numbers is called a distance magic labeling if there exists a constant ???? such that for every vertex ?????????, the sum of all its neighbors’ labels equals to ????. We call the graph ???? admitting a distance magic labeling as a distance magic graph and ???? is called the magic constant of ????. We could define a closed distance magic labeling analogously by using the closed neighbors of the vertex ????.
It has been proven that every distance magic graph has a unique magic constant, and the same applies for closed distance magic graphs. Furthermore, the existence of distance magic graphs has been verified for particular magic constants, and its inexistence have been verified for the other magic constants. In this thesis, we will discuss the analogous properties of closed distance magic graphs, which includes the existence of closed distance magic graphs based on their magic constants. We will also derive a relation between the magic constants of several classes of graphs admitting closed distance magic labelings with their order. |
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