On monophonic position sets of Cartesian and lexicographic products of graphs
The general position problem in graph theory asks for the number of vertices in a largest set $S$ of vertices of a graph $G$ such that no shortest path of $G$ contains more than two vertices of $S$. The analogous monophonic position problem is obtained from the general position problem by replacing...
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| creator | V, Ullas Chandran S Klavžar, Sandi K, Neethu P Tuite, James |
| description | The general position problem in graph theory asks for the number of vertices
in a largest set $S$ of vertices of a graph $G$ such that no shortest path of
$G$ contains more than two vertices of $S$. The analogous monophonic position
problem is obtained from the general position problem by replacing ``shortest
path" by ``induced path." This paper studies monophonic position sets in the
Cartesian and lexicographic products of graphs. Sharp lower and upper bounds
for the monophonic position number of Cartesian products are established, along
with several exact values. For the lexicographic product, the monophonic
position number is determined for arbitrary graphs. |
| doi_str_mv | 10.48550/arxiv.2412.09837 |
| format | Article |
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in a largest set $S$ of vertices of a graph $G$ such that no shortest path of
$G$ contains more than two vertices of $S$. The analogous monophonic position
problem is obtained from the general position problem by replacing ``shortest
path" by ``induced path." This paper studies monophonic position sets in the
Cartesian and lexicographic products of graphs. Sharp lower and upper bounds
for the monophonic position number of Cartesian products are established, along
with several exact values. For the lexicographic product, the monophonic
position number is determined for arbitrary graphs.</description><identifier>DOI: 10.48550/arxiv.2412.09837</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2024-12</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2412.09837$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2412.09837$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>V, Ullas Chandran S</creatorcontrib><creatorcontrib>Klavžar, Sandi</creatorcontrib><creatorcontrib>K, Neethu P</creatorcontrib><creatorcontrib>Tuite, James</creatorcontrib><title>On monophonic position sets of Cartesian and lexicographic products of graphs</title><description>The general position problem in graph theory asks for the number of vertices
in a largest set $S$ of vertices of a graph $G$ such that no shortest path of
$G$ contains more than two vertices of $S$. The analogous monophonic position
problem is obtained from the general position problem by replacing ``shortest
path" by ``induced path." This paper studies monophonic position sets in the
Cartesian and lexicographic products of graphs. Sharp lower and upper bounds
for the monophonic position number of Cartesian products are established, along
with several exact values. For the lexicographic product, the monophonic
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in a largest set $S$ of vertices of a graph $G$ such that no shortest path of
$G$ contains more than two vertices of $S$. The analogous monophonic position
problem is obtained from the general position problem by replacing ``shortest
path" by ``induced path." This paper studies monophonic position sets in the
Cartesian and lexicographic products of graphs. Sharp lower and upper bounds
for the monophonic position number of Cartesian products are established, along
with several exact values. For the lexicographic product, the monophonic
position number is determined for arbitrary graphs.</abstract><doi>10.48550/arxiv.2412.09837</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | On monophonic position sets of Cartesian and lexicographic products of graphs |
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