For a cycle graph to be self-complementary, the complement graph must have the same number of edges as its original. This can only happen when n=5, as the number of edges in G+G′=n(n−1)2, so we require n(n−1)=4n, or n2−5n=0 which only has solutions n=0,5.
Sep 25, 2016
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The simplest non-trivial self-complementary graphs are the 4-vertex path graph and the 5-vertex cycle graph. There is no known characterization of self ...
Abstract. Let G be a self-complementary graph of order p ≥ 8. It is shown that for every integer l, 3 ≤ l ≤ p − 2, G has an l-cycle. Further, if G is ...
A self-complementary graph is a graph which is isomorphic to its graph complement. The numbers of simple self-complementary graphs on n=1, 2, ... nodes are ...
Aug 3, 2023 · A graph is self-complementary if it is isomorphic to its complement. Question: How many self-complementary graphs are perfect? More precisly, ...
Hence, same degree sequence and connected, but “different” graphs. Figure 0.6: One graph contains a chordless cycle of length five while the other doesn't.
May 7, 2023 · A self-complementary graph is a graph that is isomorphic to its complement. In other words, if G is a self-complementary graph, then the vertices of G can be ...
Dec 16, 2023 · In this paper, we study the graph that is isomorphic to its complement, hence called self-complementary. The graph of order one is trivially ...
We consider only finite graphs without loops or multiple edges. Clapham [ 1] proved that every self-complementary graph (abbreviated.
A graph is self-complementary if it is isomorphic to its complement. ... True iff G has a simple cycle that goes through every vertex of the graph.