TY - JOUR
ID - 5091
TI - A graph associated to proper non-small subsemimodules of a semimodule
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Alwan, Ahmed H.
AD - Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
Y1 - 2021
PY - 2021
VL - 12
IS - 2
SP - 499
EP - 509
KW - subsemimodule
KW - small intersection graph
KW - clique number
KW - domination number
KW - independence number
DO - 10.22075/ijnaa.2021.5091
N2 - Let M be a unitary left R-semimodule where R is a commutative semiring with identity. The small intersection graph G(M) of a semimodule M is an undirected simple graph with all non-small proper subsemimodules of M as vertices and two distinct vertices N and L are adjacent if and only if N ∩ L is not small in M. In this paper, we investigate the fundamental properties of these graphs to relate the combinatorial properties of G(M) to the algebraic properties of the R-semimodule M. Determine the diameter and the girth of G(M). Moreover, we study cut vertex, clique number, domination number and independence number of the graph G(M). It is shown that the independence number of small graph is equal to the number of its maximal subsemimodules.
UR - https://ijnaa.semnan.ac.ir/article_5091.html
L1 - https://ijnaa.semnan.ac.ir/article_5091_1fcbe04dc35df6fc7c2ed2da5c66352f.pdf
ER -