{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:08Z","timestamp":1740155948659,"version":"3.37.3"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Department of Science and Technology, Government of India","award":["SR\/S4\/MS:760\/12"],"award-info":[{"award-number":["SR\/S4\/MS:760\/12"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p>A distance compatible set labeling (dcsl) of a connected graph [Formula: see text] is an injective set assignment [Formula: see text] [Formula: see text] being a non-empty ground set, such that the corresponding induced function [Formula: see text] given by [Formula: see text] satisfies [Formula: see text] for every pair of distinct vertices [Formula: see text] where [Formula: see text] denotes the path distance between [Formula: see text] and [Formula: see text] and [Formula: see text] is a constant, not necessarily an integer, depending on the pair of vertices [Formula: see text] chosen. A dcsl [Formula: see text] of [Formula: see text] is [Formula: see text]-uniform if all the constants of proportionality with respect to [Formula: see text] are equal to [Formula: see text] and if [Formula: see text] admits such a dcsl then [Formula: see text] is called a [Formula: see text]-uniform dcsl graph. The family [Formula: see text] is well-graded family, if there is a tight path between any two of its distinct sets. A learning graph is an [Formula: see text]-induced graph of a learning space. In this paper, we initiate a study on subgraphs of 1-uniform graphs which lead to the study of Knowledge Structures, Learning Spaces and Union-closed conjecture using graph theory techniques.<\/jats:p>","DOI":"10.1142\/s179383091750046x","type":"journal-article","created":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T09:29:33Z","timestamp":1498037373000},"page":"1750046","source":"Crossref","is-referenced-by-count":0,"title":["Learning graphs and 1-uniform dcsl graphs"],"prefix":"10.1142","volume":"09","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2368-6864","authenticated-orcid":false,"given":"Jinto","family":"James","sequence":"first","affiliation":[{"name":"Department of Mathematics, Central University of Kerala, Kasaragod, 671316, India"}]},{"given":"K. A.","family":"Germina","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central University of Kerala, Kasaragod, 671316, India"}]},{"given":"P.","family":"Shaini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Central University of Kerala, Kasaragod, 671316, India"}]}],"member":"219","published-online":{"date-parts":[[2017,8,16]]},"reference":[{"key":"S179383091750046XBIB001","series-title":"MRI Lecture Notes in Applied Mathematics","volume-title":"Set-valuations of Graphs and Their Applications.","volume":"2","author":"Acharya B. D.","year":"1983"},{"key":"S179383091750046XBIB002","first-page":"1","volume":"16","author":"Acharya B. D.","year":"2001","journal-title":"Bull. Allahabad Math. Soc."},{"key":"S179383091750046XBIB003","first-page":"49","volume":"1","author":"Acharya B. D.","year":"2011","journal-title":"Indian J. Math. Comput. 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