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

Document Type : Research Paper

Authors

1 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan

2 Department of Mathematics COMSATS University Islamabad, Lahore Campus, 54000, Pakistan

3 Department of Mathematics, The University of Okara, Pakistan

Abstract

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.

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References

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Transactions on Combinatorics
Volume 9, Issue 4 - Serial Number 4
December 2020
Pages 181-199

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History

  • Receive Date: 07 December 2019
  • Revise Date: 14 February 2020
  • Accept Date: 06 March 2020
  • Published Online: 01 December 2020

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