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

نویسندگان
Hanif, Muhammad Farhan ID 1
Siddiqui, Muhammad Kamran ID 2
Naeem, Muhammad ID 3
Rashid, Muhammad Aamer ID 4
Ahmad, Sarfraz ID 5

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

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

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

doi
10.22108/toc.2020.120375.1689
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