{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T04:51:09Z","timestamp":1698468669786},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,8]]},"abstract":"<jats:p>Let [Formula: see text] be an integer, and let [Formula: see text] be the set of all non-zero proper ideals of [Formula: see text]. The intersection graph of ideals of [Formula: see text], denoted by [Formula: see text], is a graph with the vertex set [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]. Let [Formula: see text] be an integer and [Formula: see text] be a [Formula: see text]-module. In this paper, we study a kind of graph structure of [Formula: see text], denoted by [Formula: see text]. It is the undirected graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. Clearly, [Formula: see text]. Let [Formula: see text] and [Formula: see text], where [Formula: see text]\u2019s are distinct primes, [Formula: see text]\u2019s are positive integers, [Formula: see text]\u2019s are non-negative integers, and [Formula: see text] for [Formula: see text] and let [Formula: see text], [Formula: see text]. The cardinality of [Formula: see text] is denoted by [Formula: see text]. Also, let [Formula: see text], [Formula: see text] and [Formula: see text] denote the independence number, the domination number and the set of all isolated vertices of [Formula: see text], respectively. We prove that [Formula: see text] and we show that if [Formula: see text] is not a null graph, then [Formula: see text] and [Formula: see text] We also compute some of its numerical invariants, namely maximum degree and chromatic index. Among other results, we determine all integer numbers [Formula: see text] and [Formula: see text] for which [Formula: see text] is Eulerian.<\/jats:p>","DOI":"10.1142\/s179383091950037x","type":"journal-article","created":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T03:08:46Z","timestamp":1557457726000},"page":"1950037","source":"Crossref","is-referenced-by-count":3,"title":["The intersection graph of ideals of \u2124m"],"prefix":"10.1142","volume":"11","author":[{"given":"S.","family":"Khojasteh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran"}]}],"member":"219","published-online":{"date-parts":[[2019,9,16]]},"reference":[{"key":"S179383091950037XBIB001","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972712001177"},{"key":"S179383091950037XBIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.745867"},{"key":"S179383091950037XBIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498815501078"},{"key":"S179383091950037XBIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811005452"},{"key":"S179383091950037XBIB005","volume-title":"A First Course in Discrete Mathematics","author":"Anderson I.","year":"2001"},{"key":"S179383091950037XBIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S179383091950037XBIB007","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.2011.4800"},{"key":"S179383091950037XBIB008","volume-title":"Selected Topics in Graph Theory","author":"Beineke L. 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