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شبهه ترنسورسالها درمربعات لاتین و k-احاطه گری در گرافها | ||
| پدافند الکترونیکی و سایبری | ||
| دوره 10، شماره 3 - شماره پیاپی 39، دی 1401، صفحه 67-75 اصل مقاله (1.14 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| نویسندگان | ||
| عادل کاظمی* 1؛ بهناز پهلوسای2 | ||
| 1دانشیار، دانشکده ریاضی، دانشگاه محقق اردبیلی، اردبیل، ایران | ||
| 2دکتر، دانشکده ریاضی، دانشگاه هوکایدو، ساپورو، ژاپن | ||
| تاریخ دریافت: 05 آبان 1400، تاریخ بازنگری: 23 آذر 1400، تاریخ پذیرش: 18 مرداد 1401 | ||
| چکیده | ||
| یک مربع لاتین از مرتبه $n$ یک آرایه $n xn$ از $n$ شئ مختلف است که در هیچ سطر وستون آن عضو تکراری موجود نباشد. در این مقاله به‌معرفی گراف‌های مربع لاتین پرداخته و سپس مسئله‌‌ی احاطه‌گری را در این گرافها را بررسی کرده و هم‌چنین ارتباط این مسئله با مفاهیم تعریف شده در مربع‌های لاتین مثل مربع‌های متعامد و $k$- ترانسورسال‌ها را مطالعه خواهیم نمود. مسئله احاطه‌گری گراف مربع لاتین، تا آن‌جائی که اطلاع داریم، به‌صورت کلی تا زمان نوشتن این مقاله در جایی مطالعه نشده است. اگرچه حالت خاصی از این مسئله، مطالعه‌ی مربع‌های لاتین دارای متعامد، یک مسئله معروف در ترکیبیات است. | ||
| کلیدواژه‌ها | ||
| مربع لاتین؛ ترنسوسال؛ شبهه - ترنسوسال؛ عدد k-احاطه کنندگی | ||
| عنوان مقاله [English] | ||
| Quasi-transversals in Latin squares and k-domination in graphs | ||
| نویسندگان [English] | ||
| Adel P. Kazemi1؛ Behnaz Pahlavsay2 | ||
| 1Associate Professor, Faculty of Mathematics, Mohaghegh Ardabili University, Ardabil, Iran | ||
| 2Ph.D., Faculty of Mathematics, Hokkaido University, Sapporo, Japan | ||
| چکیده [English] | ||
| In this paper, we first present the relation between a transversal in a Latin square with some concepts in its Latin square graph, and give an equivalent condition for a Latin square has an orthogonal mate. The most famous open problem involving Combinatorics is to find maximum number of disjoint transversals in a Latin square. So finding some family of decomposible Latin squares into disjoint transversals is our next aim. In the next section, we give an equivalent statement of a conjecture which has been attributed to Brualdi, Stein and Ryser by the concept of quasi-transversal. Finally, we prove the truth of the Rodney's conjecture for a family of graphs. | ||
| کلیدواژه‌ها [English] | ||
| Latin square, transversal, quasi-transversal, $k$-domination number | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 141 تعداد دریافت فایل اصل مقاله: 150 |
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