{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T08:09:14Z","timestamp":1769155754405,"version":"3.49.0"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> The Wiener index of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text] where the sum is taken through all unordered pairs of vertices of [Formula: see text] and [Formula: see text] is distance between two vertices [Formula: see text] and [Formula: see text] of [Formula: see text]. Let [Formula: see text] and [Formula: see text] be two graphs. For a graph [Formula: see text], let [Formula: see text] be a copy of [Formula: see text] and [Formula: see text]. The [Formula: see text]-sum [Formula: see text] is a graph with the set of vertices [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] of [Formula: see text] are adjacent if and only if [Formula: see text] or [Formula: see text], where [Formula: see text] be one of the shadowgraph [Formula: see text] or closed shadowgraph [Formula: see text]. In this paper, we reported the Wiener index of these graphs. <\/jats:p>","DOI":"10.1142\/s1793830922500689","type":"journal-article","created":{"date-parts":[[2022,3,14]],"date-time":"2022-03-14T08:22:55Z","timestamp":1647246175000},"source":"Crossref","is-referenced-by-count":5,"title":["Wiener index of sum of shadowgraphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Shanu","family":"Goyal","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics, Banasthali University, Banasthali-304022, India"}]},{"given":"Dilip","family":"Jain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government Polytechnic College, Bundi, 323001 Rajasthan, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2159-7710","authenticated-orcid":false,"given":"Vishnu Narayan","family":"Mishra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, 484 887 Madhya Pradesh, India"}]}],"member":"219","published-online":{"date-parts":[[2022,3,12]]},"reference":[{"key":"S1793830922500689BIB001","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/0095-8956(90)90136-N","volume":"48","author":"Alth\u00f6fer I.","year":"1990","journal-title":"J. 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