Let G be a graph, a subset S⊆ E (G) is called an edge hub set of G if every pair of edges e,
f∈ E (G) S are connected by a path where all internal edges are from S. The minimum …

The concept of hop hub-integrity is introduced as a new measure of the stability of a graph G
and it is defined as HhI (G)= min {| S|+ m (G− S)}, where S is hop hub set and m (G− S) is the …

The hub-integrity of a connected graph G=(V (G), E (G)) is denoted as HI (G) and defined by
HI (G)= min {| S|+ m (GS)}, where S is hub set and m (GS) is the order of a maximum …

The field of graph theory is one of the ever growing branch of mathematics. Graph theory, in
its essence can be described as the study of relations on finite sets, which are visualized …

ABSTRACT A set 𝐻 of vertices in a graph 𝐺 is a hub set of 𝐺, if for any 𝑢, 𝑣∈ 𝑉 (𝐺)⟍ 𝐻,
there is a 𝑢𝑣− path with all intermediate vertices in 𝐻. A hub set 𝐻𝑐𝑡 is a cototal hub set of …

The concept of distance majorization integrity is introduced as a new measure of the stability
of a graph G and it is dofincd as DMI (G)= min|| S|–||–m (G–S)), where S is a distance …