Distinct edge geodetic decomposition in graphs

Document Type : Original paper

Authors

1 Goverment College of Engineering, Tirunelveli

2 Bharathiyar University

Abstract

Let  G=(V,E) be a simple connected graph of order p and size q. A decomposition of a graph G  is a collection π of edge-disjoint subgraphs G1,G2,…,Gn  of G  such that every edge of G  belongs to exactly one Gi,(1≤i≤n). The decomposition  π={G1,G2,…,Gn} of a connected graph G is said to be a distinct edge geodetic decomposition if g1(Gi)≠g1(Gj),(1≤i≠j≤n). The maximum cardinality of π is called the distinct edge geodetic decomposition number of G and is denoted by πdg1(G), where g1(G) is the edge geodetic number of G. Some general properties satisfied by this concept are studied. Connected graphs of πdg1(G)≥2 are characterized and connected  graphs of order p with πdg1(G)=p−2 are characterized.

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References

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Communications in Combinatorics and Optimization
Volume 6, Issue 2
December 2021
Pages 185-196

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