fa تقابل توپولوژی با گراف در رنگ‌آمیزی جبر alg مقاله استخراج شده از پایان نامه Research Paper <span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">در این پژوهش به تعریف رنگ&shy;آمیزی گراف&shy;ها و نگاشت&shy;های رنگی می‌پردازیم و با تشریح ارکان تعریف رنگ&shy;پذیری نگاشت&shy;ها به توضیح شرایط برقراری آنها برای استفاده در زمینۀ رنگ&shy;آمیزی گراف&shy;ها می&shy;پردازیم و با بیان قضایا و لم&shy;های متعدد، نحوۀ عملکرد آنها &shy;روی گراف&shy;ها را نشان می&shy;دهیم. هم‌چنین با بیان تعریف چند نوع گراف و عدد رنگی منسوب به آنها، عدد&shy;رنگی مربوط به هر گراف به‌وسیلۀ این نگاشت&shy;ها تبیین و اثبات می&shy;کنیم. در ادامه نشان می‌داهیم عدد رنگی </span></span><em><span dir="LTR"><span style="font-family:Times New Roman,serif;"><span style="font-size:10.0pt;">n+3</span></span></span></em><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> برای نگاشت&shy;های رنگ&shy;پذیر انطباق زیادی با عدد&shy;رنگی گراف&shy;ها دارد. هم‌چنین به این سوال پاسخ داده می&shy;شود،</span></span><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"> که آیا این نگاشت&shy;ها توانایی کافی برای رنگ آمیزی هر نوع گراف را دارند؟</span></span><br> &nbsp;<br> <br> &nbsp; <strong>Introduction </strong><br> The aim of this study is studying coloring graph by colorable functions and explicating the conditions and their performance on known graphs. Fixing barriers of using the method such as the conditions of creating a function, defining the type of functions, etc. are among the main purposes of the study. To this end, at first, colorability of graphs is defined and then its elements are analyzed.<br> Definition: Let f : X &rarr; X be a graph without fixed point. f is colorable with k colors, if there is <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image002.gif" width="94" >, where all C_is do not include {f(x, x)}. Or similarly, for every &nbsp;<img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image004.gif" width="58" >, there is the equation &empty; = C_i &cap; f(C_i).<br> Then, to determine the chromatic number of graphs by these functions, all various theorems and lemmas are stated. It is shown that every graph is colored with a specific number by one of the colored functions<span dir="RTL"></span><br> <strong>Material and methods</strong><br> At first, coloring function is defined and its performance is stated. When the colored theorem is stated, which is the main element in coloring functions, the performance of the functions in coloring a graph is explored. Finally, the chromatic number of every graph by the functions is determined through some theorems and lemmas.<span dir="RTL"></span><br> <strong>Results and discussion<span dir="RTL"></span></strong><br> In this study the chromatic number of some graphs such as simple graph, triangular graph, complete graph, etc. was determined by these functions. It was shown that the performance of the functions are complicated at first, but they have a good performance and simplicity in every point.<br> <strong>Conclusion</strong><span dir="RTL"></span><br> The study concluded that:<br> - Except when you cannot define a function for a graph at all, the chromatic number of every graph is determinable in this way,<br> - The efficiency of this method in finding the chromatic number of graphs of many vertices is much easier.<br> - Users&rsquo; probability of mistake in estimating the chromatic number of graphs of many vertices is very low.<a href="./files/site1/files/71/13.pdf">./files/site1/files/71/13.pdf</a><br> &nbsp;  نگاشت رنگ‌پذیر, پوشش نقطه ای, رنگ‌آمیزی گراف, عدد رنگی Colored map, spot coating, graph coloring, color number 133 138 http://mmr.khu.ac.ir/browse.php?a_code=A-10-396-2&slc_lang=fa&sid=1 حمید عرفانیان اورعی دهرخی hamiderfanian23@yahoo.com 10031947532846004449 10031947532846004449 Yes دانشگاه دامغان، دانشکدۀ ریاضی و علوم کامپیوتر محمد ابری : magh30@um.ac.ir 10031947532846004450 10031947532846004450 No دانشگاه دامغان، دانشکدۀ ریاضی و علوم کامپیوتر بهزاد صالحیان متی کلایی mailto:ghorbanian@du.ac.ir 10031947532846004451 10031947532846004451 No دانشگاه دامغان، دانشکدۀ ریاضی و علوم کامپیوتر