tag:blogger.com,1999:blog-4344360081238823955.post2636557950714224452..comments2023-03-17T05:52:13.570-04:00Comments on Justin's Think Tank: Nerd Sniped by Nerd SnipingUnknownnoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-4344360081238823955.post-88668398518103318482013-10-12T22:08:09.313-04:002013-10-12T22:08:09.313-04:00There are many undirected graphs (of order > 2)...There are many undirected graphs (of order > 2) which contain no nodes with the same degree!<br /><br />Connect three nodes in a line, and then connect one end node to itself. The degree sequence is then (3,2,1)<br /><br />Connect 4 nodes in a line, connect the last two a second time, and then connect the last to itself, making (5,3,2,1)<br /><br />A better question would be "Do all finite simple graphs contain at least two nodes with the same degree?"Samhttps://www.blogger.com/profile/16643400888897643485noreply@blogger.com