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, … , $$ of G such that every edge of G belongs to exactly one $$(1 ≤ i ≤ n). The decomposition π = {G1, G2, … , $$} of a connected graph G is said to be an edge geodetic self decomposition, if $$($$) = $$(G) for all i(1 ≤ i ≤ n). The maximum cardinality of π is called the edge geodetic self decomposition number of G and is denoted by $$(G), where $$(G) is the edge geodetic number of G. Some general properties satisfied by this concept are studied.
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DOI : 10.1051/ro/2020073
Keywords: Edge geodetic number, edge geodetic decomposition, edge geodetic self decomposition, edge geodetic self decomposition number
@article{RO_2021__55_S1_S1935_0,
author = {John, J. and Stalin, D.},
title = {The edge geodetic self decomposition number of a graph},
journal = {RAIRO. Operations Research},
pages = {S1935--S1947},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020073},
mrnumber = {4223150},
zbl = {1469.05142},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020073/}
}
TY - JOUR AU - John, J. AU - Stalin, D. TI - The edge geodetic self decomposition number of a graph JO - RAIRO. Operations Research PY - 2021 SP - S1935 EP - S1947 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020073/ DO - 10.1051/ro/2020073 LA - en ID - RO_2021__55_S1_S1935_0 ER -
John, J.; Stalin, D. The edge geodetic self decomposition number of a graph. RAIRO. Operations Research, Tome 55 (2021), pp. S1935-S1947. doi: 10.1051/ro/2020073
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