{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:19:23Z","timestamp":1777645163553,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T00:00:00Z","timestamp":1556236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2019,4,26]]},"abstract":"<jats:p>\n                    Let G = ( V ( G), E( G)) be a simple undirected graph. The domination and average lower domination numbers are vulnerability parameters of a graph. We have investigated a refinement that involves the residual domination and average lower residual domination numbers of these parameters. The lower residual domination number, denoted by [Formula: see text], is the minimum cardinality of dominating set in G that received from the graph G where the vertex v\n                    <jats:sub>k<\/jats:sub>\n                    and all links of the vertex v\n                    <jats:sub>k<\/jats:sub>\n                    are deleted. The residual domination number of graphs G is defined as [Formula: see text]. The average lower residual domination number of G is defined by [Formula: see text]. In this paper, we define the residual domination and the average lower residual domination numbers of a graph and we present the exact values, upper and lower bounds for some graph families.\n                  <\/jats:p>","DOI":"10.3233\/fi-2019-1806","type":"journal-article","created":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T11:44:48Z","timestamp":1556279088000},"page":"379-392","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Combining the Concepts of Residual and Domination in Graphs"],"prefix":"10.1177","volume":"166","author":[{"given":"Tufan","family":"Turac\u0131","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karabuk University, 78050 Karabuk, Turkey."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aysun","family":"Ayta\u00e7","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ege University, 35100 \u0130zmir, Turkey."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,4,26]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1806","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1806","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:30Z","timestamp":1777444290000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2019-1806"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,26]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4,26]]}},"alternative-id":["10.3233\/FI-2019-1806"],"URL":"https:\/\/doi.org\/10.3233\/fi-2019-1806","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,26]]}}}