TY - JOUR
ID - 24517
TI - Zero-sum flow number of categorical and strong product of graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Rashid, Muhammad Aamer
AU - Ahmad, Sarfraz
AU - Hanif, Muhammad Farhan
AU - Siddiqui, Muhammad Kamran
AU - Naeem, Muhammad
AD - Department of Mathematics,
COMSATS University Islamabad, Lahore Campus, 54000, Pakistan
AD - Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan
AD - Department of Mathematics COMSATS University Islamabad, Lahore Campus, 54000, Pakistan
AD - Department of Mathematics, The University of Okara, Pakistan
Y1 - 2020
PY - 2020
VL - 9
IS - 4
SP - 181
EP - 199
KW - Regular graph
KW - zero-sum flow
KW - categorical product of graphs
KW - strong product graphs
DO - 10.22108/toc.2020.120375.1689
N2 - 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.
UR - https://toc.ui.ac.ir/article_24517.html
L1 - https://toc.ui.ac.ir/article_24517_97a6195eb2729b9bbe843c44360c7b64.pdf
ER -