Results 11 to 20 of about 627,001 (273)
Distant sum distinguishing index of graphs
Discrete Mathematics, 2017 Consider a positive integer $r$ and a graph $G=(V,E)$ with maximum degree $ $ and without isolated edges. The least $k$ so that a proper edge colouring $c:E\to\{1,2,\ldots,k\}$ exists such that $\sum_{e\ni u}c(e)\neq \sum_{e\ni v}c(e)$ for every pair of distinct vertices $u,v$ at distance at most $r$ in $G$ is denoted by $ '_{ ,r}(G)$.
Przybyło, Jakub
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On the neighbour sum distinguishing index of planar graphs
, 2014 22 ...
Bonamy, Marthe, Przybylo, Jakub
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Distinguishing number and distinguishing index of certain graphs [PDF]
Filomat, 2017 The distinguishing number (index) D(G) (D0(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. In this paper we compute these two parameters for some specific graphs.
Alikhani, Saeid, Soltani, Samaneh
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The Distinguishing Index of Infinite Graphs [PDF]
The Electronic Journal of Combinatorics, 2015 The distinguishing index $D^\prime(G)$ of a graph $G$ is the least cardinal $d$ such that $G$ has an edge colouring with $d$ colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number $D(G)$ of a graph $G$, which is defined with respect to vertex colourings.We derive several bounds for ...
Broere, Izak, Pilsniak, Monika
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Edge-Distinguishing Index of a Graph [PDF]
Graphs and Combinatorics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kalinowski, Rafał, Woźniak, Mariusz
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Two-distance vertex-distinguishing index of sparse graphs
Open Mathematics, 2023 The two-distance vertex-distinguishing index χd2′(G){\chi }_{d2}^{^{\prime} }\left(G) of graph GG is defined as the smallest integer kk, for which the edges of GG can be properly colored using kk colors.
He Zhengyue, Liang Li, Gao Wei
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European Journal of Combinatorics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Monika Pilśniak, Thomas Tucker
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AVD proper edge-coloring of some families of graphs
International Journal of Mathematics for Industry, 2021 Adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for the proper edge-coloring of [Formula: see text] in which no two adjacent vertices are incident to edges colored with the same set of colors.
J. Naveen
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Frontiers in Endocrinology, 2021 ObjectiveGraves’ disease (GD) and autoimmune thyroiditis (AIT) are two major causes of thyrotoxicosis that require correct diagnosis to plan appropriate treatment. The objectives of this study were to evaluate the usefulness of thyroid-related parameters
Zhiyong Wu +11 more
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List distinguishing index of graphs
, 2023 We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-identity automorphism. We show that such colouring can be chosen from any set of lists associated to the edges of a graph G, whenever the size of each list is at least $Δ-1 ...
Kwaśny, Jakub, Stawiski, Marcin
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