Neighborhub number of graphs

Let G be a graph. A neighborhub set (n-hub set) S of G is a set of vertices with the property that for any pair of vertices outside of S, there is a path between them with all intermediate vertices in S and G = S Uv∈S . The neighborhub number (n-hub number) hn(G) is then defined to be the size of a smallest neighborhub set of G. In this paper, the neighborhub number for several classes of graphs is computed, bounds in terms of other graph parameters are also determined.Emerging Sources Citation Index (ESCI)MathScinetScopu

Miscellaneous Properties Of Full Graphs

In this paper, we stablish miscellaneous properties of the full graph of a graph. We obtain characterizations of this graph. Also, we prove that for any connected graph G, the full graph of G is not separable

Hubtic number in graphs

The maximum order of partition of the vertex set $V(G)$ into hub sets is called hubtic number of $G$ and denoted by $\xi(G)$. In this paper we determine the hubtic number of some standard graphs. Also we obtain bounds for $\xi(G)$. And we characterize the class of all $(p,q)$ graphs for which $\xi(G)=p$

On hubtic and restrained hubtic of a graph

In this article, the hubtic number of the join and corona of two connected graphs is computed. The restrained hubtic number ξr(G) of a graph G is the maximum number such that we can partition V (G) into pairwise disjoint restrained hub sets. We compute the restrained hubtic number of some standard graphs. Some bounds for ξr(G) are obtained.The second author is partially supported by UGC financial assistance under no. F.510/12/DRS-II/2018(SAP-I).Publisher's Versio