Common Neighbourhood and Common Neighbourhood Domination in Fuzzy Graphs

The Common-Neighbourhood of a Graph

Abstract: The most widely used and well-known vulnerability measures of a connected graph are based on the neighbourhood concept. It takes into account neighbour-integrity, edge-integrity and accessibility number. In this work we define and examine common-neighbourhood of a connected graph as a new global connectivity measure. Our measure examines the neighbourhoods of all pairs of vertices of ...

Fuzzy T-neighbourhood spaces: Part 2 - T-neighbourhood systems

We explore a notion of fuzzy T -neighbourhood spaces, for any continuous triangular norm T , and we present on this notion a uni6ed treatment. Our theory, on one hand, generalizes the theory of Lowen (Fuzzy Sets and Systems 7 (1982) 65) from T =Min to arbitrary T , which has been the progenitor of this work, and on the other hand it is strongly related to the theory of L-neighbourhoods of H; oh...

Closed-neighbourhood anti-Sperner graphs

Configurations graphs of neighbourhood geometries

Configurations of type (κ +1)κ give rise to κ–regular simple graphs via configuration graphs. On the other hand, neighbourhood geometries of C4–free κ–regular simple graphs on κ 2 + 1 vertices turn out to be configurations of type (κ + 1)κ. We investigate which configurations of type (κ +1)κ are equal or isomorphic to the neighbourhood geometry of their configuration graph and conversely. We cl...

Forbidden graphs for degree and neighbourhood conditions

For various graph-theoretic properties P that impose upper bounds on the minimum degree or the size of a neighbourhood set, we characterize the class %(P’) (%((P’)) of graphs G such that G and all its subgraphs (subcontractions) have property P. For example, if P is “6 <xn” (6 = minimum degree, n = number of vertices, 0 <X < 1) then S(P’) = F(K,+,), the class of graphs that do not have K,,, as ...