### DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB

= http://dx.doi.org/10.20473/conmatha.v1i1.14771

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#### Abstract

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by Go_{k}H. While level k comb product graph between any graph G and H denoted by Go^{k}H.

In this research, local adjacency metric dimension of Go_{k}S_{m} graph only dependent to multiplication of the cardinality of V(G) and many of k value, while Go_{k}K_{m} graph and Go_{k}C_{m} graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of K_{m} graph or C_{m} graph. And then, local adjacency metric dimension of Go_{k}S_{m} graph only dependent to the cardinality of V(Go^{k-1}S_{m}), while Go^{k}K_{m} graph and Go^{k}C_{m} graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of K_{m} graph or C_{m} graph with cardinality of V(Go^{k-1}K_{m}) or V(Go^{k-1}C_{m}).

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#### References

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