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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Trường Đại học Đà Lạt
2023
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114425 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/830 |
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oai:scholar.dlu.edu.vn:DLU123456789-1144252023-10-27T14:46:38Z THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 Do, Nhu An 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. 2023-03-04T08:26:02Z 2023-03-04T08:26:02Z 2021 Article 0866-787X https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114425 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/830 10.37569/DalatUniversity.11.4.830(2021) en Tạp chí Khoa học Đại học Đà Lạt, Tập 11, Số 4; tr. 55-62 application/pdf Trường Đại học Đà Lạt |
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Thư viện Trường Đại học Đà Lạt |
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English |
| description |
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. |
| format |
Article |
| author |
Do, Nhu An |
| spellingShingle |
Do, Nhu An THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| author_facet |
Do, Nhu An |
| author_sort |
Do, Nhu An |
| title |
THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| title_short |
THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| title_full |
THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| title_fullStr |
THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| title_full_unstemmed |
THE STRUCTURE OF GRAPHS ON n VERTICES WITH THE DEGREE SUM OF ANY TWO NONADJACENT VERTICES EQUAL TO n-2 |
| title_sort |
structure of graphs on n vertices with the degree sum of any two nonadjacent vertices equal to n-2 |
| publisher |
Trường Đại học Đà Lạt |
| publishDate |
2023 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/114425 https://tckh.dlu.edu.vn/index.php/tckhdhdl/article/view/830 |
| _version_ |
1781718989778452480 |