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Line completion number of grid graph Pn × Pm | ||
| Communications in Combinatorics and Optimization | ||
| دوره 6، شماره 2، اسفند 2021، صفحه 299-313 اصل مقاله (399.25 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.26884.1156 | ||
| نویسندگان | ||
| Joseph Varghese Kureethara* ؛ Merin Sebastian | ||
| Christ University | ||
| چکیده | ||
| The concept of super line graph was introduced in the year 1995 by Bagga, Beineke and Varma. Given a graph with at least $r$ edges, the super line graph of index $r$, $L_r(G)$, has as its vertices the sets of $r$-edges of $G$, with two adjacent if there is an edge in one set adjacent to an edge in the other set. The line completion number $lc(G)$ of a graph $G$ is the least positive integer $r$ for which $L_r(G)$ is a complete graph. In this paper, we find the line completion number of grid graph $P_n \times P_m$ for various cases of $n$ and $m$. | ||
| کلیدواژهها | ||
| Line graph؛ Super line graph؛ Grid graph؛ Line completion number | ||
| مراجع | ||
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[12] S.A. Tapadia and B.N. Waphare, The line completion number of hypercubes, AKCE Int. J. Graphs Comb. 16 (2019), no. 1, 78–82. | ||
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