The week's pick
Reseach Article
Extreme Edge Fixed Steiner Graphs
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 178 - Number 51 |
| Year of Publication: 2019 |
| Authors: M. Perumalsamy, P. Arul Paul Sudhahar, R. Vasanthi |
10.5120/ijca2019919358
|
M. Perumalsamy, P. Arul Paul Sudhahar, R. Vasanthi . Extreme Edge Fixed Steiner Graphs. International Journal of Computer Applications. 178, 51 ( Sep 2019), 8-11. DOI=10.5120/ijca2019919358
Abstract
For a non-empty set W of vertices in a connected graph G, the Steiner distance d(W) of W is the minimum size of a connected sub graph of G containing W. S(W ) denotes the set of vertices that lies in Steiner W-trees. Steiner sets and Steiner number of a graph G was studied in [3]. A vertex v is an extreme vertex of a graph G if the sub graph induced by its neighbours is complete. The number of extreme vertices in G is its extreme order Ext(G). Extreme Steiner graphs were introduced and studied in [7]. Edge fixed Steiner sets of a graph G and the edge fixed Steiner number of G were introduced and characterized in [6]. In this paper we introduce an extreme edge fixed Steiner graph and a perfect extreme edge fixed Steiner graph. Some standard graphs are analyzed and characterized as extreme edge fixed Steiner graphs and perfect extreme edge fixed Steiner graphs. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with Ext(G) = a and se(G) = b for some edge e in G.
References
- B. Bollobas, Extremal Graph Theory, Academic press, 1978.
- F. Buckley and F. Harary,Distance in Graphs, Addison-Wesley, Redwood City, CA, 1990.
- G. Chartrand and P. Zhang,The Steiner number of a graph, Discrete Math- ematics 242 (2002) 41 - 54 DOI: 10.1016/S0012-365X(00)00456-8
- Gary Chatrand and Ping Zhang,Introduction to Graph Theory , Eighth Reprint 2012, Tata McGraw Hill Education Private Limited, New Delhi.F. Harary,Graph Theory, Addison-Wesley, 1969.
- M.Perumalsamy, P.Arul Paul Sudhahar, J.John and R.Vasanthi, Edge fixed Steiner number of a graph, International Journal of Mathematical Analysis Vol. 11, (2017), No. 16, 771 - 785 doi.org/10.12988/ijma.2017.7694.
- A.P. Santhakumaran, EXTREME STEINER GRAPHS, Discrete Mathematics, Algorithms and Applications Vol. 4, No. 2 (2012) 1250029 (11 pages)
- M.Perumalsamy, P.Arul Paul Sudhahar and R.Vasanthi, The Upper Edge Fixed Steiner Number of a Graph, International Journal of Mathematics And its Applications.,Volume 6(2A)(2018), 337 - 343.
- M.Perumalsamy, P.Arul Paul Sudhahar, R.Vasanthi and J.John, The forcing edge fixed steiner number of a graph,Journal of Statistics and Man- agement Systems, Volume 22, 2019 - Issue 1.
Index Terms
Keywords