Results 21 to 30 of about 1,106 (97)
A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs [PDF]
, 2014 The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule":
A Sebö +19 more
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A Note on the Interval Function of a Disconnected Graph
Discussiones Mathematicae Graph Theory, 2018 In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.
Changat Manoj +3 more
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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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Universal immersion spaces for edge-colored graphs and nearest-neighbor metrics [PDF]
, 2009 There exist finite universal immersion spaces for the following: (a) Edge-colored graphs of bounded degree and boundedly many colors.
Bartal, Yair, Schulman, Leonard J.
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Weak Total Resolvability In Graphs
Discussiones Mathematicae Graph Theory, 2016 A vertex v ∈ V (G) is said to distinguish two vertices x, y ∈ V (G) of a graph G if the distance from v to x is di erent from the distance from v to y.
Casel Katrin +3 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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Inverse Problem on the Steiner Wiener Index
Discussiones Mathematicae Graph Theory, 2018 The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) =∑u,v∈V (G)dG(u, v), where dG(u, v) is the distance (the length a shortest path) between the vertices u and v in G. For S ⊆ V (G), the Steiner distance d(S) of
Li Xueliang, Mao Yaping, Gutman Ivan
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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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Sharp bounds for partition dimension of generalized Möbius ladders
Open Mathematics, 2018 The concept of minimal resolving partition and resolving set plays a pivotal role in diverse areas such as robot navigation, networking, optimization, mastermind games and coin weighing.
Hussain Zafar +4 more
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