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1990•Glasgow Mathematical JournalOpen access

Graphs with near v- and e-neighbourhoods

Dalibor Fronček

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Abstract

All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges. By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraph induced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph (f) (or (xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.

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What this paper is about

All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges. By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraph induced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph (f) (or (xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.

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Available abstract

All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges. By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraph induced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph (f) (or (xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.

Key concepts: Neighbourhood (mathematics), Combinatorics, Mathematics, Vertex (graph theory), Vertex connectivity, Induced subgraph, Graph, Discrete mathematics

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