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Graphoidally Independent Infinite Cactus | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 9، شماره 3، آذر 2024، صفحه 413-423 اصل مقاله (369.08 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27745.1338 | ||
| نویسندگان | ||
| Deepti Jain* 1؛ Purnima Gupta2 | ||
| 1Department of Mathematics, Sri Venkateswara College, University of Delhi, Delhi, India | ||
| 2Adjunct Professor (Prof of Eminence), Department of Mathematics, Ramanujan College, University of Delhi, Delhi, India | ||
| چکیده | ||
| A graphoidal cover of a graph $G$ (not necessarily finite) is a collection $\psi$ of paths (not necessarily finite, not necessarily open) satisfying the following axioms: (GC-1) Every vertex of $G$ is an internal vertex of at most one path in $\psi$, and (GC-2) every edge of $G$ is in exactly one path in $\psi$. The pair $(G, \psi)$ is called a graphoidally covered graph and the paths in $\psi$ are called the $\psi$-edges of $G$. In a graphoidally covered graph $(G, \psi)$, two distinct vertices $u$ and $v$ are $\psi$-adjacent if they are the ends of an open $\psi$-edge. A graphoidally covered graph $(G, \psi)$ in which no two distinct vertices are $\psi$-adjacent is called $\psi$-independent and the graphoidal cover $\psi$ is called a totally disconnecting graphoidal cover of $G$. Further, a graph possessing a totally disconnecting graphoidal cover is called a graphoidally independent graph. The aim of this paper is to establish complete characterization of graphoidally independent infinite cactus. | ||
| کلیدواژهها | ||
| Graphoidal Cover of a Graph؛ Graphoidally Covered Graphs؛ Graphoidally Independent Graphs؛ Cactus | ||
| مراجع | ||
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