@article {
author = {JOHN, J. and Stalin, D.},
title = {Distinct edge geodetic decomposition in graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {6},
number = {2},
pages = {185-196},
year = {2021},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2020.26638.1126},
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 $\pi$ of edge-disjoint subgraphs $G_{1}, G_{2} ,\dots, G_{n}$ of $G$ such that every edge of $G$ belongs to exactly one $G_{i},(1\leq i\leq n)$. The decomposition $\pi=\{G_{1},G_{2},\dots,G_{n}\}$ of a connected graph $G$ is said to be a distinct edge geodetic decomposition if $g_{1}(G_{i})\neq g_{1}(G_{j}),(1\leq i\neq j\leq n)$. The maximum cardinality of $\pi$ is called the distinct edge geodetic decomposition number of $G$ and is denoted by $\pi_{dg_{1}}(G)$, where $g_{1}(G)$ is the edge geodetic number of $G$. Some general properties satisfied by this concept are studied. Connected graphs of $\pi_{dg_{1}}(G)\geq2$ are characterized and connected graphs of order $p$ with $\pi_{dg_{1}}(G)=p-2$ are characterized.},
keywords = {Edge geodetic number,minimum edge geodetic set,Distinct edge geodetic decomposition,Distinct edge geodetic decomposition number,Star decomposition},
url = {https://comb-opt.azaruniv.ac.ir/article_14114.html},
eprint = {https://comb-opt.azaruniv.ac.ir/article_14114_9555441344465ec52e1ff6583ab21566.pdf}
}