Results 1 to 10 of about 634,558 (159)
Neighbor Sum Distinguishing Index [PDF]
Graphs and Combinatorics, 2012 We consider proper edge colorings of a graph G using colors of the set {1, . . . , k}. Such a coloring is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G
Flandrin, Evelyne +4 more
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Trees with Distinguishing Index Equal Distinguishing Number Plus One
Discussiones Mathematicae Graph Theory, 2020 The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid +3 more
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Distinguishing index of Kronecker product of two graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 The distinguishing index D'(G) of a graph G is the least integer d such that G has an edge labeling with d labels that is preserved only by a trivial automorphism. The Kronecker product G x H of two graphs G and H is the graph with vertex set V(G) x V(H)
Saeid Alikhani, Samaneh Soltani
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Distinguishing Number and Distinguishing Index of the Join of Two Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 The distinguishing number (index) D(G) (D'(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 study the distinguishing number and the
Saeid Alikhani, Samaneh Soltani
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The distinguishing number and the distinguishing index of line and graphoidal graph(s)
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing number (index) () of a graph is the least integer such that has a vertex labeling (edge labeling) with labels that is preserved only by a trivial automorphism.
Saeid Alikhani, Samaneh Soltani
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The chromatic distinguishing index of certain graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 The distinguishing index of a graph , denoted by , is the least number of labels in an edge coloring of not preserved by any non-trivial automorphism. The distinguishing chromatic index of a graph is the least number such that has a proper edge coloring ...
Saeid Alikhani, Samaneh Soltani
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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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The Distinguishing Number and Distinguishing Index of the Lexicographic Product of Two Graphs
Discussiones Mathematicae Graph Theory, 2018 The distinguishing number (index) D(G) (D′(G)) of a graph G is the least integer d such that G has a vertex labeling (edge labeling) with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid, Soltani Samaneh
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A Note on Neighbor Expanded Sum Distinguishing Index
Discussiones Mathematicae Graph Theory, 2017 A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction.
Flandrin Evelyne +4 more
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On the neighbour sum distinguishing index of planar graphs
, 2014 22 ...
Bonamy, Marthe, Przybylo, Jakub
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