TY - JOUR
ID - 14114
TI - Distinct edge geodetic decomposition in graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - JOHN, J.
AU - Stalin, D.
AD - Goverment College of Engineering, Tirunelveli
AD - Bharathiyar University
Y1 - 2021
PY - 2021
VL - 6
IS - 2
SP - 185
EP - 196
KW - Edge geodetic number
KW - minimum edge geodetic set
KW - Distinct edge geodetic decomposition
KW - Distinct edge geodetic decomposition number
KW - Star decomposition
DO - 10.22049/cco.2020.26638.1126
N2 - 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.
UR - https://comb-opt.azaruniv.ac.ir/article_14114.html
L1 - https://comb-opt.azaruniv.ac.ir/article_14114_9555441344465ec52e1ff6583ab21566.pdf
ER -