{"id":5775,"date":"2026-02-20T04:38:18","date_gmt":"2026-02-19T20:38:18","guid":{"rendered":"https:\/\/transactions.nast.ph\/?p=5775"},"modified":"2026-03-26T14:54:32","modified_gmt":"2026-03-26T06:54:32","slug":"on-hierarchical-circulant-networks","status":"publish","type":"post","link":"https:\/\/transactions.nast.ph\/?p=5775","title":{"rendered":"On Hierarchical Circulant Networks"},"content":{"rendered":"\n<p class=\"has-text-align-center\">Felix P. Muga II<br>Department of Mathematics<br>Ateneo de Manila University<\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"http:\/\/doi.org\/10.57043\/transnastphl.1999.5775\">http:\/\/doi.org\/10.57043\/transnastphl.1999.5775<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-1 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p><strong>Abstract<\/strong><\/p>\n\n\n\n<p>A fundamental consideration in the design of massively parallel and distributed computer systems is the topology of the processors (or the vertices, in graph theory). Well accepted designs are those that can be recursively decomposed, providing a way for the implementation of recursive algorithms. Hierarchical networks are recursively decomposable. In this paper, we examined the conditions for a network to be hierarchical. We limited our study to undirected and connected circulant networks.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h5 class=\"wp-block-heading\">Keywords<\/h5>\n\n\n<div class=\"taxonomy-post_tag wp-block-post-terms\"><span class=\"wp-block-post-terms__prefix\"><br><\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=circulant-networks\" rel=\"tag\">Circulant networks<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=decomposition\" rel=\"tag\">decomposition<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=edge-preserving-connected\" rel=\"tag\">edge-preserving; connected<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=graph-isomorphism-subgraph\" rel=\"tag\">graph isomorphism; subgraph<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=hierarchical\" rel=\"tag\">hierarchical<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=recursivey-decomposed\" rel=\"tag\">Recursivey decomposed<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=undirected\" rel=\"tag\">undirected<\/a><\/div><\/div>\n<\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\"  class=\"wp-block-file__embed\" data=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_8_On-Hierarchical-Circulant-Networks.pdf\" type=\"application\/pdf\" style=\"width:100%;height:1090px\" aria-label=\"Embed of TNP 1999 (21)_8_On Hierarchical Circulant Networks.\"><\/object><a id=\"wp-block-file--media-f05f105c-5729-4fbb-baad-9e09265eabe9\" href=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_8_On-Hierarchical-Circulant-Networks.pdf\">TNP 1999 (21)_8_On Hierarchical Circulant Networks<\/a><a href=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_8_On-Hierarchical-Circulant-Networks.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-f05f105c-5729-4fbb-baad-9e09265eabe9\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Felix P. Muga II<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[819],"tags":[872,871,873,875,874,876,877],"class_list":{"0":"post-5775","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-1999-technical-papers","7":"tag-circulant-networks","8":"tag-decomposition","9":"tag-edge-preserving-connected","10":"tag-graph-isomorphism-subgraph","11":"tag-hierarchical","12":"tag-recursivey-decomposed","13":"tag-undirected","14":"czr-hentry"},"_links":{"self":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5775"}],"collection":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5775"}],"version-history":[{"count":3,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5775\/revisions"}],"predecessor-version":[{"id":6049,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5775\/revisions\/6049"}],"wp:attachment":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}