Bibliographic Details
| Title: |
On intersection graph of ideals of a near-ring in terms of its essential ideals. |
| Authors: |
Pal, Pavel (AUTHOR) ju.pavel86@gmail.com, Jana, Jyotirmoy (AUTHOR) jyotirmoyjana.1996@gmail.com |
| Source: |
Discussiones Mathematicae: General Algebra & Applications. 2025, Vol. 45 Issue 2, p387-405. 19p. |
| Subjects: |
Ideals (Algebra), Intersection graph theory, Semirings (Mathematics), Graph connectivity, Complete graphs, Graph theory |
| Abstract: |
Let N be a near-ring and I(N) denote the set of all non-trivial (i.e., non-zero proper) ideals of N. In this paper, the intersection graph of ideals of N has been introduced as a simple undirected graph denoted by G(N) whose vertex set is I(N) and two vertices I and J are adjacent if and only if I ≠ J and I ∩ J ≠ {0}. The graph G(N) has been studied mainly using the direct sum decomposition and the essential ideals of N. Here, some neces- sary and sufficient conditions for G(N) to be connected and complete have been obtained. Under some restrictions on N and G(N), some graph parameters such as chromatic number, independence number, domination number, hull number, geodetic number as well as some graphical properties of G(N) such as being chordal, star etc. have been obtained. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
