Characterizing Graphs via Edge Geodetic Domination Number
DOI:
https://doi.org/10.26713/cma.v17i1.3443Abstract
Dominance in graphs is the crucial aspect of graph theory that has been thoroughly examined.
Consider a graph G1(V1,E1) with S ⊆ V1 in such a way that atleast one vertex in the set is
contiguous to the vertices that do not belong to the set then S is said to be the dominating set.
In other words, it can be said that the set of vertices belonging to S and S′ has atleast a single
neighbor in each other. Any set A ⊆ G1 having all edges of G comprised in a geodesic unite
a couple of vertices in A is claimed to be an EG-set of G1. The EG-number, indicated by the
symbol ge(G), is the lowest order of its EG-set. A ge-set of G or EG-basis of G, is any EG-set of
order ge(G). If a collection of vertices“D in G is together an EG-set and a dominant set then D”is
considered an EG-dominating set. The EG-dominance number of the EG-dominating set is its
minimum cardinal number represented as γge(G). With this work, we explore the EG-dominance
number of varied graphs namely antiprism graph An, alternate pentagonal snake A(PSn), Bistar
graph, ladder graph, jewel graph and Helm graph.
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