Bi-Edge Metric Dimension of Graphs
Keywords:
Bi-Metric Dimension, Edge Metric Dimension, Edge Detour Dimension, Bi-Edge Metric DimensionAbstract
Given a connected G = (V(G),E(G)) graph. The main problem in graph metric dimensions is calculating the metric dimensions and their characterization. In this research, a new dimension concept is introduced, namely a bi-edge metric dimension of graph which is a development of the concpet of bi-metric graphs with the innovation of bi-metric graph representations to become the bi-edge metric graph representations. In this case, what is meant by bi-edge metric and edge detour. If there is a set in G that causes every edge in G has a different bi-edge metric representation in G, then that set is called the biedge metric resolving set. The minimum cardinality of the bi-edge metric resolving set graphs is called the bi-edge metric dimension of G graph, denoted by edimb(G). The spesific purpose of this research is to apply the concept of bi-edge metric dimensions to special graphs, such as cycle, complete, star and path can be obtained.References
Kelenc, A., Tratnik, N., and Yero, I.G.: Uniquely Identifying The Edge
of a Graph: The Edge Metric Dimension. Discrete Applied Mathematics.
Vol. 251, 204-220 (2018).
Santhakumaran, A.P., and Athisayanathan, S.: On Edge Detour Graphs. Discussiones Mathematicae Graph Theory, 30(1), 155-174 (2010).
Raghavendra, A., Sooryanarayana, B., and Hedge, C.: Bi-metric Dimension of Graphs. British Journal of Mathematics & Computer Science, 4(18), 2699-2714 (2014).
Sundusia, J. K. and Rinurwati: The Complement Bi-metric Dimension of Graphs. AIP Publishing, Vol. 2641 (2022).
Iswadi, H., Baskoro, E.T., Salman, A.N.M., and Simanjuntak, R.: The
Resolving Graph of Amalgamation of Cycles. Far East Journal of
Mathematical Sciences (FJMS), 41(1): 19-31 (2010).
Rinurwati., Sundusia, J.K., Haryadi, T.I., and Maharani, F.D.:The Complement Bimetric Dimension of Corona Graphs. AIP Conference Proceedings. (Pre-published).
Rinurwati., Suprajitno, H., and Slamin: On Metric Dimension of EdgeCorona Graphs. Far East Journal of Mathematical Sciences, 102(5), 965-978 (2017).
Santhakumaran, A.P., Titus, P., and Arumugam: The Vertex Detour
Number of a Graph. AKCE J. Graphs. Combin. 4(1): 99-112 (2007)
