The vulnerability measures on a connected graph which are mostly used and known are based on the Neighbourhood concept. Neighbour-integrity, edge-integrity and accessibility number are some of these measures. In this work we define and examine the Common-neighbourhood of a connected graph as a new global connectivity measure. It takes account the neighbourhoods of all pairs of vertices. We show that, for connected graphs G1 and G2 of order n, if the dominating number of G1 is bigger than the dominating number of G2, then the common- neighbourhood of G1 is less than the common-neighbourhood of G2. We prove some theorems on common-neighbourhood of a graph.
@article{22464,
title = {The common-neighbourhood of a graph},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v35i1.22464},
language = {EN},
url = {http://dml.mathdoc.fr/item/22464}
}
Aytac, Aysun. The common-neighbourhood of a graph. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v35i1.22464. http://gdmltest.u-ga.fr/item/22464/