Name
Abstract | ||
|---|---|---|
A graph G is said to be k-gamma t-critical if the total domination number gamma t(G) = k and gamma t(G + uv) < k for every uv E(G). A k-gamma c-critical graph G is a graph with the connected domination number gamma c - k and gamma c (G + uv) < k for every uv E(G). Further, a k-tvc graph is a graph with gamma t(G) - k and gamma t(G - v) < k for all v E V(G), where v is not a support vertex (i.e. all neighbors of v have degree greater than one). A 2 -connected graph G is said to be k-cvc if gamma c(G) = k and gamma c(G - v) < k for all v E V(G). In this paper, we prove that connected k-gamma t-critical graphs and k-gamma c-critical graphs are the same if and only if 3 <= k <= 4. For k >= 5, we concentrate on the class of connected k -gamma t -critical graphs G with gamma c(G) = k and the class of k - gamma c-critical graphs G with gamma(G) = k. We show that these classes intersect but they do not need to be the same. Further, we prove that 2 -connected k-tvc graphs and k-tvc graphs are the same if and only if 3 <= k <= 4. Similarly, for k >= 5, we focus on the class of 2 -connected k-tvc graphs G with N(G) = k and the class of 2 -connected k-cvc graphs G with gamma t(G) = k. We finish this paper by showing that these classes do not need to be the same. |
Year | Venue | Field |
|---|---|---|
2016 | AUSTRALASIAN JOURNAL OF COMBINATORICS | Connected domination,Graph,Combinatorics,Mathematics |
DocType | Volume | ISSN |
Journal | 65 | 2202-3518 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| P. Kaemawichanurat | 1 | 0 | 0.34 |
| Lou Caccetta | 2 | 19 | 3.38 |
| Nawarat Ananchuen | 3 | 36 | 7.22 |