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Zero-sum flow number of categorical and strong product of graphs | ||
| Transactions on Combinatorics | ||
| مقاله 27، دوره 9، شماره 4، اسفند 2020، صفحه 181-199 اصل مقاله (267.88 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.120375.1689 | ||
| نویسندگان | ||
| Muhammad Aamer Rashid1؛ Sarfraz Ahmad2؛ Muhammad Farhan Hanif1؛ Muhammad Kamran Siddiqui* 3؛ Muhammad Naeem4 | ||
| 1Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan | ||
| 2Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan | ||
| 3Department of Mathematics COMSATS University Islamabad, Lahore Campus, 54000, Pakistan | ||
| 4Department of Mathematics, The University of Okara, Pakistan | ||
| چکیده | ||
| A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum $k$-flow if the absolute values of edges are less than $k$. We define the zero-sum flow number of $G$ as the least integer $k$ for which $G$ admitting a zero sum $k$-flow.? In this paper we gave complete zero-sum flow and zero sum numbers for categorical and strong product of two graphs namely cycle and paths. | ||
| کلیدواژه‌ها | ||
| regular graph؛ zero-sum flow؛ categorical product of graphs؛ strong product graphs | ||
| مراجع | ||
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