Results 1 to 10 of about 1,116 (99)
On the general position number of two classes of graphs
Open Mathematics, 2022 The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic.
Yao Yan, He Mengya, Ji Shengjin
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On Antipodal and Diametrical Partial Cubes
Discussiones Mathematicae Graph Theory, 2021 We prove that any diametrical partial cube of diameter at most 6 is antipodal. Because any antipodal graph is harmonic, this gives a partial answer to a question of Fukuda and Handa [Antipodal graphs and oriented matroids, Discrete Math.
Polat Norbert
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Independence Number and Packing Coloring of Generalized Mycielski Graphs
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
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Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae Graph Theory, 2021 Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle ...
McKee Terry A.
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Asymptotic Behavior of the Edge Metric Dimension of the Random Graph
Discussiones Mathematicae Graph Theory, 2021 Given a simple connected graph G(V,E), the edge metric dimension, denoted edim(G), is the least size of a set S ⊆ V that distinguishes every pair of edges of G, in the sense that the edges have pairwise different tuples of distances to the vertices of S.
Zubrilina Nina
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Hosoya properties of the commuting graph associated with the group of symmetries
Main Group Metal Chemistry, 2021 A vast amount of information about distance based graph invariants is contained in the Hosoya polynomial. Such an information is helpful to determine well-known distance based molecular descriptors.
Abbas Ghulam +4 more
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The Proper Diameter of a Graph
Discussiones Mathematicae Graph Theory, 2020 A proper edge-coloring of a graph is a coloring in which adjacent edges receive distinct colors. A path is properly colored if consecutive edges have distinct colors, and an edge-colored graph is properly connected if there exists a properly colored path
Coll Vincent +4 more
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The normalized distance Laplacian
Special Matrices, 2021 The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of ...
Reinhart Carolyn
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Comparing Eccentricity-Based Graph Invariants
Discussiones Mathematicae Graph Theory, 2020 The first and second Zagreb eccentricity indices (EM1 and EM2), the eccentric distance sum (EDS), and the connective eccentricity index (CEI) are all recently conceived eccentricity-based graph invariants, some of which found applications in chemistry ...
Hua Hongbo, Wang Hongzhuan, Gutman Ivan
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On kernels by rainbow paths in arc-coloured digraphs
Open Mathematics, 2021 In 2018, Bai, Fujita and Zhang [Discrete Math. 341 (2018), no. 6, 1523–1533] introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph DD, which is a subset SS of vertices of DD such that (aa) there exists no ...
Li Ruijuan, Cao Yanqin, Zhang Xinhong
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