{"id":2993,"date":"2025-10-27T05:34:44","date_gmt":"2025-10-27T05:34:44","guid":{"rendered":"https:\/\/cvsc.upcebu.edu.ph\/?post_type=project&p=2993"},"modified":"2026-01-27T05:35:24","modified_gmt":"2026-01-27T05:35:24","slug":"perfect-zero-divisor-graphs-of-the-ring-of-gaussian-integers-modulo-pn","status":"publish","type":"project","link":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/project\/perfect-zero-divisor-graphs-of-the-ring-of-gaussian-integers-modulo-pn\/","title":{"rendered":"Perfect Zero-Divisor Graphs of the Ring of Gaussian Integers Modulo\u00a0pn"},"content":{"rendered":"

[et_pb_section fb_built=”1″ theme_builder_area=”post_content” _builder_version=”4.27.5″ _module_preset=”default”][et_pb_row column_structure=”1_3,2_3″ _builder_version=”4.27.4″ _module_preset=”default” custom_padding=”40px|||||” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_column type=”1_3″ _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_heading title=”Perfect Zero-Divisor Graphs of the Ring of Gaussian Integers Modulo p\u207f” _builder_version=”4.27.5″ _module_preset=”default” title_font=”|700|on||||||” title_text_color=”gcid-body-color” title_font_size=”41px” custom_margin=”|-828px|25px|||” hover_enabled=”0″ global_colors_info=”{%22gcid-body-color%22:%91%22title_text_color%22%93}” theme_builder_area=”post_content” sticky_enabled=”0″][\/et_pb_heading][et_pb_image src=”http:\/\/cvsc.upcebu.edu.ph\/wp-content\/uploads\/2026\/01\/Romeo-Journal-of-Physics.jpg” title_text=”JPCS FC 0519″ _builder_version=”4.27.5″ _module_preset=”default” hover_enabled=”0″ box_shadow_style=”preset2″ global_colors_info=”{}” theme_builder_area=”post_content” sticky_enabled=”0″][\/et_pb_image][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_text _builder_version=”4.27.5″ _module_preset=”default” text_font_size=”15px” text_line_height=”1.1em” custom_padding=”118px|||||” hover_enabled=”0″ global_colors_info=”{}” theme_builder_area=”post_content” header_line_height=”1.2em” sticky_enabled=”0″]<\/p>\n

Lead Researcher(s): <\/strong>Francis S. Escaros <\/span><\/span>and Marie Cris A. Bulay-og<\/span><\/span>
Status:<\/strong> Published<\/p>\n

Abstract\/summary:<\/strong> The zero-divisor graph of a ring\u00a0<\/span>R<\/i>\u00a0is a graph whose vertex set is the set of nonzero zero-divisors of\u00a0<\/span>R<\/i>\u00a0where two vertices\u00a0<\/span>u<\/i>\u00a0and\u00a0<\/span>\u03c5<\/i>\u00a0are connected by an edge if and only if\u00a0<\/span>u\u03c5<\/i>\u00a0= 0. In [6], Smith studied the perfectness of the zero-divisor graph of the ring \u2124<\/span>n<\/sub><\/i>. By definition, a perfect graph is a graph\u00a0<\/span>G<\/i>\u00a0for which every induced subgraph of\u00a0<\/span>G<\/i>\u00a0has chromatic number equal to its clique number. In this paper, we extend the work of Smith to the zero-divisor graphs of the ring \u2124<\/span>p<\/i><\/sub>n [<\/span>i<\/i>], where\u00a0<\/span>p<\/i>\u00a0is a prime in \u2124,\u00a0<\/span>n<\/i>\u00a0is a positive integer and\u00a0<\/span>i<\/i>\u00a0is an imaginary unit in the ring \u2102 of complex numbers.<\/span><\/span><\/p>\n

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Lead Researcher(s): Francis S. Escaros and Marie Cris A. Bulay-ogStatus: Published Abstract\/summary: The zero-divisor graph of a ring\u00a0R\u00a0is a graph whose vertex set is the set of nonzero zero-divisors of\u00a0R\u00a0where two vertices\u00a0u\u00a0and\u00a0\u03c5\u00a0are connected by an edge if and only if\u00a0u\u03c5\u00a0= 0. In [6], Smith studied the perfectness of the zero-divisor graph of the ring \u2124n. […]<\/p>\n","protected":false},"author":7,"featured_media":0,"template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"project_category":[37,34],"project_tag":[],"class_list":["post-2993","project","type-project","status-publish","hentry","project_category-journals-books-and-reports","project_category-recent-publications"],"_links":{"self":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/2993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project"}],"about":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/types\/project"}],"author":[{"embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":2,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/2993\/revisions"}],"predecessor-version":[{"id":2996,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/2993\/revisions\/2996"}],"wp:attachment":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/media?parent=2993"}],"wp:term":[{"taxonomy":"project_category","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project_category?post=2993"},{"taxonomy":"project_tag","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project_tag?post=2993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}