THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2
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...
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| Format: | Bài viết |
| Jezik: | English |
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Trường Đại học Đà Lạt
2023
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| Online dostop: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114425 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/830 |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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| Izvleček: | 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. |
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