Graph Theory and its Applications Group \u2014 Mathematics Research Center<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&family=DM+Mono:wght@300;400;500&family=Outfit:wght@300;400;500;600&display=swap\" rel=\"stylesheet\">\n<script>MathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n<style>body{background:#eee;padding:2rem;margin:0;}<\/style>\n<\/head>\n<body>\n\n\n<style>\n:root {\n --cream:#F5F0E8;--ink:#1A1610;--rust:#B84A2F;--gold:#C99A2E;\n --slate:#3D4A5C;--mist:#E8EDF4;--rule:#C8BFA8;\n --green:#52B788;--green-bg:#EDF4EC;--green-dk:#2D6A4F;\n --garamond:'EB Garamond',Georgia,serif;\n --mono:'DM 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.grp-members{grid-template-columns:1fr;}\n .grp-lower-grid{grid-template-columns:1fr;gap:2rem;}\n .ga-item{grid-template-columns:44px 1fr;}\n}\n<\/style>\n\n<div class=\"grp-block\">\n <div class=\"grp-accent graph\"><\/div>\n\n <div class=\"grp-hero graph\">\n <a class=\"grp-hero-back\" href=\"\/index.php\/research\/\">\n <svg viewBox=\"0 0 10 10\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.5\"><path d=\"M7 1L3 5l4 4\"\/><\/svg>\n Research Groups\n <\/a>\n <div class=\"grp-hero-tag\">Mathematics Research Center \u00b7 ASOIU<\/div>\n <h1>Graph Theory and its Applications Group<\/h1>\n <p class=\"grp-hero-sub\">Spectral graph theory, graph entropy, and algebraic combinatorics<\/p>\n <\/div>\n\n <div class=\"grp-body\">\n <div class=\"grp-label\">About the Group<\/div>\n <div class=\"grp-desc\">\n <p>The Graph Theory and its Applications Group investigates structural and spectral properties of graphs, with a strong emphasis on real-world modelling and applications. Research spans algebraic and topological aspects of graph theory \u2014 including Castelnuovo\u2013Mumford regularity, simplicial complexes, and Laplacian eigenvectors \u2014 as well as graph entropy, network assortativity, and hierarchical structures in complex networks.<\/p><p>A distinctive feature of the group’s work is the bridge it builds between pure combinatorics and applied settings, including biochemical network alignment, chemical graph theory, and wireless communication. The group maintains active collaborations with researchers in combinatorial commutative algebra, bioinformatics, and information theory.<\/p>\n <\/div>\n\n <div class=\"grp-label grp-mt\">Members<\/div>\n <div class=\"grp-members\">\n <a class=\"grp-member-card\" href=\"\/index.php\/turkerbiyikoglu\/\">\n <div class=\"grp-member-placeholder\">TB<\/div>\n <div class=\"grp-member-info\">\n <div class=\"grp-member-name\">T\u00fcrker B\u0131y\u0131ko\u011flu<\/div>\n <div class=\"grp-member-role\">Senior Researcher<\/div>\n <\/div>\n <\/a>\n <\/div>\n\n <div class=\"grp-lower-grid\">\n \n <div>\n <div class=\"grp-label grp-mt\">Recent Activities<\/div>\n <div id=\"ga-list-graph\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n\n \n <div>\n <div class=\"grp-label grp-mt\">Announcements<\/div>\n <div id=\"ga-ann-graph\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n<script>\n(function(){\n var SITE = window.location.origin;\n var GROUP_TAG_ID = 26; \/\/ Tag ID for Graph Theory[cite: 1]\n var MONTHS = ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'];\n\n var SEMINAR_CATS = [6, 7, 8, 15];\n var SEMINAR_MAP = {\n 6: {cls:'seminar', label:'General Seminar'},\n 7: {cls:'seminar', label:'Research Seminar'},\n 8: {cls:'seminar', label:'Student Seminar'},\n 15: {cls:'conference', label:'Conference'},\n 'default': {cls:'default', label:'Seminar'}\n };\n\n var NEWS_CATS = [19, 20, 21, 22, 23, 28];\n var NEWS_MAP = {\n 19: {cls:'publication', label:'Publication'},\n 20: {cls:'seminar-abroad', label:'Seminar abroad'},\n 21: {cls:'new-member', label:'New member'},\n 23: {cls:'award', label:'Award'},\n 28: {cls:'milestone', label:'Milestone'},\n 22: {cls:'visitor', label:'Visitor'},\n 'default': {cls:'default', label:'News'}\n };\n\n function getBadge(cats, map){\n if(cats) for(var i=0;i<cats.length;i++) if(map[cats[i]]) return map[cats[i]];\n return map['default'];\n }\n\n function renderList(posts, map, listEl, emptyMsg){\n if(!posts.length){\n listEl.innerHTML = '<div class=\"grp-placeholder\"><span class=\"grp-placeholder-icon\">\ud83d\udcc5<\/span>' + emptyMsg + '<\/div>';\n return;\n }\n var html = '<ul class=\"ga-list\">';\n posts.forEach(function(p){\n var d = new Date(p.date);\n var badge = getBadge(p.categories, map);\n var title = p.title.rendered.replace(\/<[^>]+>\/g,'');\n html += '<li class=\"ga-item\"><div class=\"ga-date-box\"><span class=\"ga-date-day\">' + d.getDate() + '<\/span><span class=\"ga-date-mon\">' + MONTHS[d.getMonth()] + '<\/span><\/div>' +\n '<div class=\"ga-content\"><span class=\"nb-badge ' + badge.cls + '\">' + badge.label + '<\/span><div class=\"ga-title\">' +\n (p.link ? 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0;display:flex;gap:.8rem;}\n.nb-skel-box{background:rgba(26,22,16,.07);border-radius:2px;animation:nb-pulse 1.5s infinite;}\n.nb-skel-d{height:18px;width:52px;flex-shrink:0;}\n.nb-skel-l1{height:9px;width:35%;margin-bottom:5px;}\n.nb-skel-l2{height:13px;width:85%;}\n@keyframes nb-pulse{0%,100%{opacity:.4}50%{opacity:.7}}\n\n@media(max-width:680px){\n .grp-hero{padding:2rem 1.5rem 1.8rem;}\n .grp-body{padding:2rem 1.5rem;}\n .grp-members{grid-template-columns:1fr;}\n .grp-lower-grid{grid-template-columns:1fr;gap:2rem;}\n .ga-item{grid-template-columns:44px 1fr;}\n}\n<\/style>\n\n<div class=\"grp-block\">\n <div class=\"grp-accent graph\"><\/div>\n\n <div class=\"grp-hero graph\">\n <a class=\"grp-hero-back\" href=\"\/index.php\/research\/\">\n <svg viewBox=\"0 0 10 10\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.5\"><path d=\"M7 1L3 5l4 4\"\/><\/svg>\n Research Groups\n <\/a>\n <div class=\"grp-hero-tag\">Mathematics Research Center \u00b7 ASOIU<\/div>\n <h1>Graph Theory and its Applications Group<\/h1>\n <p class=\"grp-hero-sub\">Spectral graph theory, graph entropy, and algebraic combinatorics<\/p>\n <\/div>\n\n <div class=\"grp-body\">\n <div class=\"grp-label\">About the Group<\/div>\n <div class=\"grp-desc\">\n <p>The Graph Theory and its Applications Group investigates structural and spectral properties of graphs, with a strong emphasis on real-world modelling and applications. Research spans algebraic and topological aspects of graph theory \u2014 including Castelnuovo\u2013Mumford regularity, simplicial complexes, and Laplacian eigenvectors \u2014 as well as graph entropy, network assortativity, and hierarchical structures in complex networks.<\/p><p>A distinctive feature of the group’s work is the bridge it builds between pure combinatorics and applied settings, including biochemical network alignment, chemical graph theory, and wireless communication. The group maintains active collaborations with researchers in combinatorial commutative algebra, bioinformatics, and information theory.<\/p>\n <\/div>\n\n <div class=\"grp-label grp-mt\">Members<\/div>\n <div class=\"grp-members\">\n <a class=\"grp-member-card\" href=\"\/index.php\/turkerbiyikoglu\/\">\n <div class=\"grp-member-placeholder\">TB<\/div>\n <div class=\"grp-member-info\">\n <div class=\"grp-member-name\">T\u00fcrker B\u0131y\u0131ko\u011flu<\/div>\n <div class=\"grp-member-role\">Senior Researcher<\/div>\n <\/div>\n <\/a>\n <\/div>\n\n <div class=\"grp-lower-grid\">\n \n <div>\n <div class=\"grp-label grp-mt\">Recent Activities<\/div>\n <div id=\"ga-list-graph\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n\n \n <div>\n <div class=\"grp-label grp-mt\">Announcements<\/div>\n <div id=\"ga-ann-graph\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n<script>\n(function(){\n var SITE = window.location.origin;\n var GROUP_TAG_ID = 26; \/\/ Tag ID for Graph Theory[cite: 1]\n var MONTHS = ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'];\n\n var SEMINAR_CATS = [6, 7, 8, 15];\n var SEMINAR_MAP = {\n 6: {cls:'seminar', label:'General Seminar'},\n 7: {cls:'seminar', label:'Research Seminar'},\n 8: {cls:'seminar', label:'Student Seminar'},\n 15: {cls:'conference', label:'Conference'},\n 'default': {cls:'default', label:'Seminar'}\n };\n\n var NEWS_CATS = [19, 20, 21, 22, 23, 28];\n var NEWS_MAP = {\n 19: {cls:'publication', label:'Publication'},\n 20: {cls:'seminar-abroad', label:'Seminar abroad'},\n 21: {cls:'new-member', label:'New member'},\n 23: {cls:'award', label:'Award'},\n 28: {cls:'milestone', label:'Milestone'},\n 22: {cls:'visitor', label:'Visitor'},\n 'default': {cls:'default', label:'News'}\n };\n\n function getBadge(cats, map){\n if(cats) for(var i=0;i<cats.length;i++) if(map[cats[i]]) return map[cats[i]];\n return map['default'];\n }\n\n function renderList(posts, map, listEl, emptyMsg){\n if(!posts.length){\n listEl.innerHTML = '<div class=\"grp-placeholder\"><span class=\"grp-placeholder-icon\">\ud83d\udcc5<\/span>' + emptyMsg + '<\/div>';\n return;\n }\n var html = '<ul class=\"ga-list\">';\n posts.forEach(function(p){\n var d = new Date(p.date);\n var badge = getBadge(p.categories, map);\n var title = p.title.rendered.replace(\/<[^>]+>\/g,'');\n html += '<li class=\"ga-item\"><div class=\"ga-date-box\"><span class=\"ga-date-day\">' + d.getDate() + '<\/span><span class=\"ga-date-mon\">' + MONTHS[d.getMonth()] + '<\/span><\/div>' +\n '<div class=\"ga-content\"><span class=\"nb-badge ' + badge.cls + '\">' + badge.label + '<\/span><div class=\"ga-title\">' +\n (p.link ? 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