Open AccessLine Graph Associated to Graph of a Near-Ring with Respect to an Ideal
Author(s) -
Moytri Sarmah,
Kuntala Patra
Publication year - 2021
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.52.2021.3326
Subject(s) - combinatorics , mathematics , distance regular graph , complement graph , graph power , line graph , discrete mathematics , regular graph , graph , vertex (graph theory) , edge transitive graph , simplex graph , windmill graph , neighbourhood (mathematics) , butterfly graph , voltage graph , mathematical analysis
Let N be a near-ring and I be an ideal of N. The graph of N with respect to I is a graph with V (N ) as vertex set and any two distinct vertices x and y are adjacent if and only if xNy ⊆ I oryNx ⊆ I. This graph is denoted by GI(N). We define the line graph of GI(N) as a graph with each edge of GI (N ) as vertex and any two distinct vertices are adjacent if and only if their corresponding edges share a common vertex in the graph GI (N ). We denote this graph by L(GI (N )). We have discussed the diameter, girth, clique number, dominating set of L(GI(N)). We have also found conditions for the graph L(GI(N)) to be acycle graph.