http://pco.iis.nsk.su/grapp/index.php?title=(a,d)-Face_antimagic_graph&feed=atom&action=history(a,d)-Face antimagic graph - История изменений2024-03-29T09:26:54ZИстория изменений этой страницы в викиMediaWiki 1.39.3http://pco.iis.nsk.su/grapp/index.php?title=(a,d)-Face_antimagic_graph&diff=7228&oldid=prevGlk: 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: «'''<math>(a,d)</math>-Face antimagic graph''' --- <math>(a,d)</math>-граневый антимагический граф. A connected plane graph <math>G = (V,E…»</p>
<p><b>Новая страница</b></p><div>'''<math>(a,d)</math>-Face antimagic graph''' --- <math>(a,d)</math>-граневый<br />
антимагический граф. <br />
<br />
A connected plane graph <math>G = (V,E,F)</math> is said to be '''<math>(a,d)</math>-face antimagic''' if there exist positive integers <math>a,b</math> and a bijection<br />
<br />
<math>g: \; E(G) \rightarrow \{1,2, \ldots, |E(G)|\}</math><br />
<br />
such that the induced mapping <math>w_{g}^{\ast}: \; F(G) \rightarrow W</math> is<br />
also a bijection, where <math>W = \{w^{\ast}(f): \;f \in F(G)\} = \{a,a+d,<br />
\ldots, a+(|F(G)| - 1)d\}</math> is the set of weights of a face. If <math>G =<br />
(V,B,F)</math> is <math>(a,d)</math>-face antimagic and <math>g: \; E(G) \rightarrow \{1,2,<br />
\ldots, |E(G)|\}</math> is the corresponding bijective mapping of <math>G</math>, then <math>g</math> is<br />
said to be an <math>(a,d)</math>-face antimagic labeling of <math>G</math>.<br />
<br />
The weight <math>w^{\ast}(f)</math> of a face <math>f \in F(G)</math> under an edge labeling<br />
<br />
<math>g: \; E(G) \rightarrow \{1,2, \ldots, |E(G)|\}</math><br />
<br />
is the sum of the labels of edges surrounding that face.</div>Glk