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Edge domination in graphs of cubes

Bohdan Zelinka (2002)

Czechoslovak Mathematical Journal

The signed edge domination number and the signed total edge domination number of a graph are considered; they are variants of the domination number and the total domination number. Some upper bounds for them are found in the case of the n -dimensional cube Q n .

Edge maximal C 2 k + 1 -edge disjoint free graphs

M.S.A. Bataineh, M.M.M. Jaradat (2012)

Discussiones Mathematicae Graph Theory

For two positive integers r and s, 𝓖(n;r,s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f(n;r,s) = max{𝓔(G):G ∈ 𝓖(n;r,s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we determine f(n;r,2k+1) and characterize the edge maximal members in 𝓖(n;r,2k+1).

Edge shift distance between trees

Bohdan Zelinka (1992)

Archivum Mathematicum

Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances.

Edge-colouring of graphs and hereditary graph properties

Samantha Dorfling, Tomáš Vetrík (2016)

Czechoslovak Mathematical Journal

Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph G , a hereditary graph property 𝒫 and l ≥ 1 we define χ 𝒫 , l ' ( G ) to be the minimum number of colours needed to properly colour the edges of G , such that any subgraph of G induced by edges coloured by (at most) l colours is in 𝒫 . We present a necessary and sufficient condition for the existence of χ 𝒫 , l ' ( G ) . We focus on edge-colourings of graphs with respect to the hereditary properties...

Edge-domatic numbers of cacti

Bohdan Zelinka (1991)

Mathematica Bohemica

The edge-domatic number of a graph is the maximum number of classes of a partition of its edge set into dominating sets. This number is studied for cacti, i.e. graphs in which each edge belongs to at most one circuit.

Edit distance measure for graphs

Tomasz Dzido, Krzysztof Krzywdziński (2015)

Czechoslovak Mathematical Journal

In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for g ( n , l ) , the biggest number k guaranteeing that there exist l graphs on n vertices, each two having edit distance at least k . By edit distance of two graphs G , F we mean the number of edges needed to be added to or deleted from graph G to obtain graph F . This new extremal number g ( n , l ) is closely linked to the edit distance of graphs. Using probabilistic methods we show that g ( n , l ) is close...

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