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Study of Positioning Accuracy Parameters in Selected Configurations of a Modular Industrial Robot-Part 1. [PDF]

Sensors (Basel)
Suszyński M, Wiśniewski M, Wojciechowicz K, Trączyński M, Butlewski M, Cernohlavek V, Talar R.   +6 more
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Phylogenetic network classes through the lens of expanding covers. [PDF]

J Math Biol
Francis A, Marchei D, Steel M.
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Path 3-(edge-)connectivity of lexicographic product graphs

Discrete Applied Mathematics, 2020
This paper studies path 3-connectivity \(\pi_3\) and path 3-edge-connectivity \(\omega_3\) of lexicographic product graphs. If \(G\) is a 2-connected graph and \(H\) is a graph with \(n\) vertices, it is shown that \(\pi_3(G\circ H)\ge n\). Moreover, \(\omega_3(G\circ H)\ge3\lfloor n/2\rfloor\) if \(n\) is even while \(\omega_3(G\circ H)\ge3\lfloor n/2\
Ma, Tianlong, Wang, Jinling, Zhang, Mingzu, Liang, Xiaodong   +3 more
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Antimagicness of Lexicographic Product Graph G[Pn]

Acta Mathematicae Applicatae Sinica, English Series, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Ying-yu, Dong, Guang-hua, Wang, Ning
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Coupon coloring of lexicographic product of graphs

The Art of Discrete and Applied Mathematics, 2022
Summary: A \(k\)-coupon coloring of a graph \(G\) without isolated vertices is an assignment of colors from \([k]=\{1,2,\dots,k\}\) to the vertices of \(G\) such that the neighborhood of every vertex of \(G\) contains vertices of all colors from \([k]\).
Thankachan, Reji, Rajamani, Pavithra
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Convex Sets in Lexicographic Products of Graphs

Graphs and Combinatorics, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anand, Bijo S., Changat, Manoj, Klavžar, Sandi, Peterin, Iztok   +3 more
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[1, k]-Domination Number of Lexicographic Products of Graphs

Bulletin of the Malaysian Mathematical Sciences Society, 2020
Let \(G = (V, E)\) be a graph. Let \(k\) be a positive integer. A subset \(D\) of vertices of a graph \(G\) is \([1, k]\)-dominating if every vertex not in \(D\) can have at least one neighbor in \(D\) and at most \(k\) neighbors in \(D\). \(\gamma_{[1,k]}(G)\) denotes the cardinality of a smallest \([1, k]\)-dominating set. A \([1, k]\)-dominating set
Narges Ghareghani, Iztok Peterin, Pouyeh Sharifani   +2 more
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SECURE DOMINATING SETS IN THE LEXICOGRAPHIC PRODUCT OF GRAPHS

Advances and Applications in Discrete Mathematics, 2019
Summary: Let \(G=(V(G), E(G))\) be a simple graph. A set \(S\subseteq V(G)\) is a dominating (total dominating) set of \(G\) if for every \(v\in V(G)\backslash S\) (resp. \(v\in V(G)\)), there exists \(u\in S\) such that \(uv\in E(G)\). A dominating (total dominating) set \(S\) of \(G\) is a secure dominating (resp. secure total dominating) set of \(G\)
Canoy, Sergio R. jun., Canoy, Seanne Abigail E., Cruzate, Marlon F.   +2 more
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Path-connectivity of lexicographic product graphs

International Journal of Computer Mathematics, 2014
Dirac showed that in a -connected graph there is a path through all the k vertices. The k-path-connectivity of a graph G, which is a generalization of Dirac's notion, was introduced by Hager in 1986. Denote by the lexicographic product of two graphs G and H. In this paper, we prove that for any two connected graphs G and H. Moreover, the
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Omega Indices of Strong and Lexicographic Products of Graphs

Current Organic Synthesis
Background: The degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant.
Medha Itagi Huilgol, Grace Divya D'Souza, Ismail Naci Cangul   +2 more
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