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Distinct edge geodetic decomposition in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 6، شماره 2، اسفند 2021، صفحه 185-196 اصل مقاله (397.22 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26638.1126 | ||
| نویسندگان | ||
| J. JOHN* 1؛ D. Stalin2 | ||
| 1Goverment College of Engineering, Tirunelveli | ||
| 2Bharathiyar University | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Edge geodetic number؛ minimum edge geodetic set؛ Distinct edge geodetic decomposition؛ Distinct edge geodetic decomposition number؛ Star decomposition | ||
| مراجع | ||
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