@article{An_2021, place={Dalat, Vietnam}, title={THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2}, volume={11}, url={https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/830}, DOI={10.37569/DalatUniversity.11.4.830(2021)}, abstractNote={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&gt;=3 is an odd number then alpha(G)=2 and G is a disconnected graph; for n&gt;=4 is an even number then 2=&lt;alpha(G)&lt;=(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&lt;=k&lt;=(n-2)/2. In particular, when k=0 then G is an (n-2)/2-Regular graph.}, number={4}, journal={Dalat University Journal of Science}, author={An, Do Nhu}, year={2021}, month={Oct.}, pages={55–62} }