{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:36:20Z","timestamp":1760229380573,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T00:00:00Z","timestamp":1654732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008875","name":"Shanghai Institute of Technology","doi-asserted-by":"publisher","award":["10120K226052-A06"],"award-info":[{"award-number":["10120K226052-A06"]}],"id":[{"id":"10.13039\/501100008875","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let DSn(d) denote the set of all doubly symmetric primitive digraphs of order n with d loops, where d is an integer and 1\u2264d\u2264n. In this paper, we determine the upper bounds for the m-competition indices(generalized competition indices) of DSn(d), where 1\u2264m\u2264n. If n and d satisfy that n is odd and d is odd, or n\u22642d\u22122 and d is even such that d\u22652, then the upper bounds for the m-competition indices of DSn(d) can be reached, where 1\u2264m\u2264n.<\/jats:p>","DOI":"10.3390\/sym14061192","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T02:01:44Z","timestamp":1655085704000},"page":"1192","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Generalized Competition Indices of Doubly Symmetric Primitive Digraphs with d Loops"],"prefix":"10.3390","volume":"14","author":[{"given":"Danmei","family":"Chen","sequence":"first","affiliation":[{"name":"College of Sciences, Shanghai Institute of Technology, Shanghai 201418, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangjun","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brualdi, R.A., and Ryser, H.J. 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