Advances and Applications in Discrete Mathematics
Volume 19, Issue 1, Pages 33 - 49
(January 2018) http://dx.doi.org/10.17654/AADMJan2018_033_049 |
|
FORCING SUBSETS FOR SOME TYPES OF CONVEX SETS IN A GRAPH
Roxanne L. Arco and Sergio R. Canoy, Jr.
|
Abstract: Let G be a connected graph. Given any two vertices u and v of G, the set consists of all those vertices lying on a longest u-v path. A set S is a detour convex set if for A tolled walk T between distinct vertices u and v of G is a walk of the form where in which and are the only neighbors of u and v in T, respectively. The toll interval is the set of vertices in G that lie on some u-v walk. A subset is toll convex (or t-convex) if for all
In this paper, we define and study the concepts of detour convexity number, toll convexity number, forcing subset for a maximum detour convex (maximum toll convex) set, and the forcing detour convexity (forcing toll convexity) number of a graph. In particular, we study these concepts in the join and corona of graphs. |
Keywords and phrases: detour convex set, toll convex set, forcing detour convexity number, forcing toll convexity number. |
|
Number of Downloads: 376 | Number of Views: 4585 |
|