Results 31 to 40 of about 5,516,987 (160)
Edge-partitions of graphs and their neighbor-distinguishing index
Discrete Mathematics, 2017 Bojan Vučković
exaly +2 more sources
The Distinguishing Numbers and the Distinguishing Indexes of Cayley Graphs
Journal of Applied and Industrial Mathematics, 2021 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 investigate the distinguishing number and the distinguishing index of Cayley graphs.
Alikhani, S., Soltani, S.
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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
Evelyne Flandrin +4 more
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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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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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The distinguishing index of connected graphs without pendant edges
Ars Math. Contemp., 2020 We consider edge colourings, not necessarily proper. The distinguishing index D ′( G ) of a graph G is the least number of colours in an edge colouring that is preserved only by the identity automorphism. It is known that D ′( G ) ≤ Δ for every countable,
W. Imrich +3 more
semanticscholar +1 more source
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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On a Total Version of 1-2-3 Conjecture
Discussiones Mathematicae Graph Theory, 2020 A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set {1, . . . , k}. These colors can be used to distinguish adjacent vertices of G. There are many possibilities of such a distinction.
Baudon Olivier +5 more
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Rectangular Cavity Sensor for Distinguishing Between Normal and High-Drivability-Index Gasolines
IEEE Access, 2020 The Drivability Index (DI) of gasoline is a measure of fuel performance of engine operations. Therefore, distinguishing a gasoline of specific DI in advance is useful for improving engine efficiency and maintenance.
Chong Hyun Lee +2 more
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On the Neighbour Sum Distinguishing Index of Graphs with Bounded Maximum Average Degree [PDF]
Graphs and Combinatorics, 2017 A proper edge k-colouring of a graph $$G=(V,E)$$G=(V,E) is an assignment $$c:E\rightarrow \{1,2,\ldots ,k\}$$c:E→{1,2,…,k} of colours to the edges of the graph such that no two adjacent edges are associated with the same colour.
H. Hocquard, J. Przybylo
semanticscholar +2 more sources