http://pco.iis.nsk.su/grapp/index.php?title=(a,d)-Face_antimagic_graph&feed=atom&action=history (a,d)-Face antimagic graph - История изменений 2024-03-29T09:26:54Z История изменений этой страницы в вики MediaWiki 1.39.3 http://pco.iis.nsk.su/grapp/index.php?title=(a,d)-Face_antimagic_graph&diff=7228&oldid=prev Glk: Новая страница: «'''<math>(a,d)</math>-Face antimagic graph''' --- <math>(a,d)</math>-граневый антимагический граф. A connected plane graph <math>G = (V,E…» 2011-04-27T07:18:02Z <p>Новая страница: «&#039;&#039;&#039;&lt;math&gt;(a,d)&lt;/math&gt;-Face antimagic graph&#039;&#039;&#039; --- &lt;math&gt;(a,d)&lt;/math&gt;-граневый антимагический граф. A connected plane graph &lt;math&gt;G = (V,E…»</p> <p><b>Новая страница</b></p><div>&#039;&#039;&#039;&lt;math&gt;(a,d)&lt;/math&gt;-Face antimagic graph&#039;&#039;&#039; --- &lt;math&gt;(a,d)&lt;/math&gt;-граневый<br /> антимагический граф. <br /> <br /> A connected plane graph &lt;math&gt;G = (V,E,F)&lt;/math&gt; is said to be &#039;&#039;&#039;&lt;math&gt;(a,d)&lt;/math&gt;-face antimagic&#039;&#039;&#039; if there exist positive integers &lt;math&gt;a,b&lt;/math&gt; and a bijection<br /> <br /> &lt;math&gt;g: \; E(G) \rightarrow \{1,2, \ldots, |E(G)|\}&lt;/math&gt;<br /> <br /> such that the induced mapping &lt;math&gt;w_{g}^{\ast}: \; F(G) \rightarrow W&lt;/math&gt; is<br /> also a bijection, where &lt;math&gt;W = \{w^{\ast}(f): \;f \in F(G)\} = \{a,a+d,<br /> \ldots, a+(|F(G)| - 1)d\}&lt;/math&gt; is the set of weights of a face. If &lt;math&gt;G =<br /> (V,B,F)&lt;/math&gt; is &lt;math&gt;(a,d)&lt;/math&gt;-face antimagic and &lt;math&gt;g: \; E(G) \rightarrow \{1,2,<br /> \ldots, |E(G)|\}&lt;/math&gt; is the corresponding bijective mapping of &lt;math&gt;G&lt;/math&gt;, then &lt;math&gt;g&lt;/math&gt; is<br /> said to be an &lt;math&gt;(a,d)&lt;/math&gt;-face antimagic labeling of &lt;math&gt;G&lt;/math&gt;.<br /> <br /> The weight &lt;math&gt;w^{\ast}(f)&lt;/math&gt; of a face &lt;math&gt;f \in F(G)&lt;/math&gt; under an edge labeling<br /> <br /> &lt;math&gt;g: \; E(G) \rightarrow \{1,2, \ldots, |E(G)|\}&lt;/math&gt;<br /> <br /> is the sum of the labels of edges surrounding that face.</div> Glk