Sigma chromatic numbers of the middle graph of some families of graphs

Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ...

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Main Authors: Manamtam, Jay-R, Garciano, Agnes, Tolentino, Mark Anthony C
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Published: Archīum Ateneo 2022
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Online Access:https://archium.ateneo.edu/mathematics-faculty-pubs/218
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1219&context=mathematics-faculty-pubs
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spelling ph-ateneo-arc.mathematics-faculty-pubs-12192022-11-23T02:04:12Z Sigma chromatic numbers of the middle graph of some families of graphs Manamtam, Jay-R Garciano, Agnes Tolentino, Mark Anthony C Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic number of G and is denoted by σ(G). In this study, we investigate sigma coloring in relation to a unary graph operation called middle graph. We will show that the sigma chromatic number of the middle graph of any path, cycle, sunlet graph, tadpole graph, ladder graph, or triangular snake graph is 2 except for some small cases. We also determine the sigma chromatic number of the middle graph of stars. 2022-01-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/218 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1219&context=mathematics-faculty-pubs Mathematics Faculty Publications Archīum Ateneo sigma coloring middle graph Mathematics Physical Sciences and Mathematics
institution Ateneo De Manila University
building Ateneo De Manila University Library
continent Asia
country Philippines
Philippines
content_provider Ateneo De Manila University Library
collection archium.Ateneo Institutional Repository
topic sigma coloring
middle graph
Mathematics
Physical Sciences and Mathematics
spellingShingle sigma coloring
middle graph
Mathematics
Physical Sciences and Mathematics
Manamtam, Jay-R
Garciano, Agnes
Tolentino, Mark Anthony C
Sigma chromatic numbers of the middle graph of some families of graphs
description Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic number of G and is denoted by σ(G). In this study, we investigate sigma coloring in relation to a unary graph operation called middle graph. We will show that the sigma chromatic number of the middle graph of any path, cycle, sunlet graph, tadpole graph, ladder graph, or triangular snake graph is 2 except for some small cases. We also determine the sigma chromatic number of the middle graph of stars.
format text
author Manamtam, Jay-R
Garciano, Agnes
Tolentino, Mark Anthony C
author_facet Manamtam, Jay-R
Garciano, Agnes
Tolentino, Mark Anthony C
author_sort Manamtam, Jay-R
title Sigma chromatic numbers of the middle graph of some families of graphs
title_short Sigma chromatic numbers of the middle graph of some families of graphs
title_full Sigma chromatic numbers of the middle graph of some families of graphs
title_fullStr Sigma chromatic numbers of the middle graph of some families of graphs
title_full_unstemmed Sigma chromatic numbers of the middle graph of some families of graphs
title_sort sigma chromatic numbers of the middle graph of some families of graphs
publisher Archīum Ateneo
publishDate 2022
url https://archium.ateneo.edu/mathematics-faculty-pubs/218
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1219&context=mathematics-faculty-pubs
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