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Bilangan Pembeda Tanpa Titik Terisolasi Graf W_n⊙K_1dan F_n⊙K_1
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Let be a graph and be an ordered subset of the vertex set og graph The representation of a vertex in with respect to is defined as , where is the distance between vertex and for all $ The set is called a resolving set of if the representation of every vertex in is distinct. A resolving set with the minimum cardinality is called a basis of and the cardinality of a basis of is the metric dimension of the graph . A vertex in is called an isolated vertex if there are no edges incident to . A resolving set is called a non-isolated resolving set if the subgraph induced by does not contain isolated vertices. A non-isolated resolving set with the minimum cardinality is called an -basis of , and the number of its members is called the non-isolated resolving number of , nonated by .
In this paper, we discuss non-isolated resolving numbers of a graph obtained from the corona product of two graphs. The corona product of graph and graph , denoted by , is a graph obtained by taking one copy of and as many copies of as there are vertices in , then connecting every vertex from the -th copy of to the -th vertex in . The results show that if is a wheel graph or a fan graph, then the non-isolated resolving number of the corona product depends on the number of vertices in the graph
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Title: Bilangan Pembeda Tanpa Titik Terisolasi Graf W_n⊙K_1dan F_n⊙K_1
Description:
Let be a graph and be an ordered subset of the vertex set og graph The representation of a vertex in with respect to is defined as , where is the distance between vertex and for all $ The set is called a resolving set of if the representation of every vertex in is distinct.
A resolving set with the minimum cardinality is called a basis of and the cardinality of a basis of is the metric dimension of the graph .
A vertex in is called an isolated vertex if there are no edges incident to .
A resolving set is called a non-isolated resolving set if the subgraph induced by does not contain isolated vertices.
A non-isolated resolving set with the minimum cardinality is called an -basis of , and the number of its members is called the non-isolated resolving number of , nonated by .
In this paper, we discuss non-isolated resolving numbers of a graph obtained from the corona product of two graphs.
The corona product of graph and graph , denoted by , is a graph obtained by taking one copy of and as many copies of as there are vertices in , then connecting every vertex from the -th copy of to the -th vertex in .
The results show that if is a wheel graph or a fan graph, then the non-isolated resolving number of the corona product depends on the number of vertices in the graph.
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