Distances between graphs under edge operations
نویسندگان
چکیده
منابع مشابه
Distances between graphs under edge operations
We investigate three metrics on the isomorphism classes of graphs derived from elementary edge operations: the edge move, rotation and slide distances. We derive relations between the metrics, and bounds on the distance between arbitrary graphs and between arbitrary trees. We also consider the sensitivity of the metrics to various graph operations. Correspondence to: Wayne Goddard Dept of Compu...
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For two edge-induced subgraphs F and H of the same size in a graph G, the subgraph H can be obtained from F by an edge jump if there exist four distinct vertices u, v, w, and x in G such that uv ~ E(F), wx ~ E(G)-E(F), and H = F-uv + wx. The subgraph F is j-transformed into H ifH can be obtained from F by a sequence of edge jumps. Necessary and sufficient conditions are presented for a graph G ...
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Various measures of distance between (the isomorphism classes of) two graphs have been proposed. These include measures proposed by Zelinka [6],[7], Baláž, Koča, Kvasńıčka & Sekanina [1] and Johnson [4]. Further, there is the edge rotation distance of Chartrand, Saba & Zou [3] and the edge shift distance of Johnson [5]. It is on the latter two that we build. For terminology and notation not exp...
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A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u, v, and w such that uv ∈ E(G), uw 6∈ E(G), and H = G − uv + uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u, v, w, and x such that uv ∈ E(G), wx 6∈ E(G), and H = G − uv + wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G i...
متن کاملThe irregularity of graphs under graph operations
The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑ uv∈E(G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and symmetric difference. ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00073-6