Hub-integrity of splitting graph and duplication of graph elements

The hub-integrity of a graph G = (V (G), E(G)) is denoted as HI(G) and defined by HI(G) = min{|S| + m(G − S), S is a hub set of G}, where m(G − S) is the order of a maximum component of G − S. In this paper, we discuss hub-integrity of splitting graph and duplication of an edge by vertex and duplication of vertex by an edge of some graphs.Publisher's Versio

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 $\xi(G)=p$

D-Integrity and E-Integrity Numbers in Graphs

Inspired by the definition of integrity and the alternative formulations for integrity, we investigate the D−Integrity and E−Integrity numbers of a graph in the present study. The D-Integrity number of a graph G is denoted by DIk(G) defined as: DIk(G) = ∑ p Dk (G), and the E -Integrity number of a graph G, is denoted by E Il (G) defined as: E Il (G) = ∑ p El (G). In this paper, we establish k=1 l=0 the general formulas for the D−Integrity and E−Integrity numbers of some classes of graphs. Also, some properties of D−Integrity and E−Integrity numbers are established