Results on the inverse majority domination and majority independence number of a graph

In this article,the relationship between Inverse Majority Domination number γ −1 M (G) and Majority Independence number βM(G) of a graph G is discussed for some classes of graphs. In particular, γ −1 M (G) and βM(G) for cubic and cubic bipartite graph are studied with examples. Also characterization theorem for this relation and some results are determined.Publisher's Versio

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 $\xi(G)=p$

The Graphs Whose Sum of Global Connected Domination Number and Chromatic Number is 2n-5

A subset S of vertices in a graph G = (V,E) is a dominating set if every vertex in V-S is adjacent to atleast one vertex in S. A dominating set S of a connected graph G is called a connected dominating set if the induced sub graph < S > is connected. A set S is called a global dominating set of G if S is a dominating set of both G and . A subset S of vertices of a graph G is called a global connected dominating set if S is both a global dominating and a connected dominating set. The global connected domination number is the minimum cardinality of a global connected dominating set of G and is denoted by γgc(G). In this paper we characterize the classes of graphs for which γgc(G) + χ(G) = 2n-5 and 2n-6 of global connected domination number and chromatic number and characterize the corresponding extremal graphs

Inverse Domination Numbers and Disjoint Domination Numbers of Graphs under Some Binary Operations

Abstract In this note, we investigate the inverse domination numbers and the disjoint pair domination numbers of graphs resulting from the join, corona and composition of graphs Mathematics Subject Classification: 05C6

Integrity of Generalized Transformation Graphs

The values of vulnerability helps the network designers to construct such a communication network which remains stable after some of its nodes or communication links are damaged. The transformation graphs considered in this paper are taken as model of the network system and it reveals that, how network can be made more stable and strong. For this purpose the new nodes are inserted in the network. This construction of new network is done by using the definition of generalized transformation graphs of a graphs. Integrity is one of the best vulnerability parameter. In this paper, we investigate the integrity of generalized transformation graphs and their complements. Also, we find integrity of semitotal point graph of combinations of basic graphs. Finally, we characterize few graphs having equal integrity values as that of generalized transformation graphs of same structured graphs

Compressions, Graphs, and Hyperreflexivity

AbstractIn this note we extend the ideas in [11] to prove reflexivity and especially hyperreflexivity results that pertain to compressions rather than summands. These results in turn are relevant for some remarkable classes of operators