Results 21 to 30 of about 187 (132)
Strong Geodetic Problem in Networks
Discussiones Mathematicae Graph Theory, 2020 In order to model certain social network problems, the strong geodetic problem and its related invariant, the strong geodetic number, are introduced.
Manuel Paul +4 more
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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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A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs
Analysis and Geometry in Metric Spaces, 2022 The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin–Lu– Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a generalization of ...
Akamatsu Tomoya
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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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Discussiones Mathematicae Graph Theory, 2020 If S = (a1, a2, . . .) is a non-decreasing sequence of positive integers, then an S-packing coloring of a graph G is a partition of V (G) into sets X1, X2, . . .
Brešar Boštjan +3 more
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, 2013 In this paper we define a new monoid construction under crossed products for given monoids. We also present a generating set and a relator set for this product. Finally, we give the necessary and sufficient conditions for the regularity of it. MSC: 05C10,
Cangül, İ. N. +3 more
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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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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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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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Detour index of a class of unicyclic graphs
, 2010 The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the ...
Qi Xuli, Bo Zhou
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