document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475379>Question 475379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that every path is gracefull. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326408 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=326408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Label a path with three vertices:\r<BR>\n" );
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document.write( "1--3--2\r<BR>\n" );
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document.write( "A path with four vertices:\r<BR>\n" );
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document.write( "1--4--2--3\r<BR>\n" );
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document.write( "A path with five vertices:\r<BR>\n" );
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document.write( "1--5--2--4--3\r<BR>\n" );
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document.write( "In general, label an n-sided graph with the numbers 1, n, 2, n-1, 3, n-2,..., in which the differences between consecutive nodes are n-1, n-2, ..., 1, hence, graceful.\r<BR>\n" );
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document.write( "The following website gives more information about graceful graphs:<BR>\n" );
document.write( "http://mathworld.wolfram.com/GracefulGraph.html </SPAN>\n" );
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