Results 21 to 30 of about 140 (88)
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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The mixed metric dimension of flower snarks and wheels
Open Mathematics, 2021 New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks Jn{J}_{n} and wheels Wn{W}_{n}. It is proved
Danas Milica Milivojević
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Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
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Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Discussiones Mathematicae Graph Theory, 2020 A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths.
Liu Weijun +3 more
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The chromatic sum of a graph: history and recent developments
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 30, Page 1563-1573, 2004., 2004 The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive ...
Ewa Kubicka
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Discussiones Mathematicae Graph Theory, 2021 In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
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Conditional resolvability in graphs: a survey
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 38, Page 1997-2017, 2004., 2004 For an ordered set W = {w1, w2, …, wk} of vertices and a vertex v in a connected graph G, the code of v with respect to W is the k‐vector cW(v) = (d(v, w1), d(v, w2), …, d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have distinct codes with respect to W.
Varaporn Saenpholphat, Ping Zhang
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The hull number of an oriented graph
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 36, Page 2265-2275, 2003., 2003 We present characterizations of connected graphs G of order n ≥ 2 for which h+(G) = n. It is shown that for every two integers n and m with 11≤n−≤m≤(n2), there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number G.
Gary Chartrand +2 more
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A cospectral construction for the generalized distance matrix
Special MatricesThe generalized distance matrix of a graph is a matrix in which the (i,j)\left(i,j)th entry is a function, ff, of the distance between vertex ii and vertex jj.
Friesen Ori +5 more
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