TY - JOUR
AU - An, Do Nhu
TI - THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2
PY - 2021/10/04
Y2 - 2023/11/30
JF - Dalat University Journal of Science
JA - DLU JOS
VL - 11
IS - 4
LA - en
DO - 10.37569/DalatUniversity.11.4.830(2021)
UR - https://doi.org/10.37569/DalatUniversity.11.4.830(2021)
SP - 55-62
AB - Let G be an undirected simple graph on n vertices and sigma2(G)=n-2 (degree sum of any two non-adjacent vertices in G is equal to n-2) and alpha(G) be the cardinality of an maximum independent set of G. In G, a vertex of degree (n-1) is called total vertex. We show that, for n>=3 is an odd number then alpha(G)=2 and G is a disconnected graph; for n>=4 is an even number then 2=<alpha(G)<=(n+2)/2, where if alpha(G)=2 then G is a disconnected graph, otherwise G is a connected graph, G contains k total vertices and n-k vertices of degree delta=(n-2)/2, where 0<=k<=(n-2)/2. In particular, when k=0 then G is an (n-2)/2-Regular graph.
ER -