Zero-sum flow number of categorical and strong product of graphs
Publish place: Transactions on Combinatorics، Vol: 9، Issue: 4
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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JR_COMB-9-4_001
تاریخ نمایه سازی: 14 اردیبهشت 1400
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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Authors
Muhammad Aamer Rashid
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, ۵۴۰۰۰, Pakistan
Sarfraz Ahmad
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, ۵۴۰۰۰, Pakistan
Muhammad Farhan Hanif
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, ۵۴۰۰۰, Pakistan
Muhammad Kamran Siddiqui
Department of Mathematics COMSATS University Islamabad, Lahore Campus, ۵۴۰۰۰, Pakistan
Muhammad Naeem
Department of Mathematics, The University of Okara, Pakistan