Zero-sum flow number of categorical and strong product of graphs

Rashid, Muhammad Aamer; Ahmad, Sarfraz; Hanif, Muhammad Farhan; Siddiqui, Muhammad Kamran; Naeem, Muhammad

doi:10.22108/toc.2020.120375.1689

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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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Zero-sum flow number of categorical and strong product of graphs