Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2

Let G be a nontrivial connected graph and letc: V (G) → be a vertex coloring ofG, where adjacent vertices may have the same color. For a vertexv ofG, the color sumσ(v) ofv is the sum of the colors of the vertices adjacent tov. The coloringc is said to be a sigma coloring ofG ifσ(u)σ(v) wheneveru and...

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Main Authors: Manamtam, Jay R.A., Garciano, Agnes D., Tolentino, Mark Anthony C.
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Published: Archīum Ateneo 2023
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Online Access:https://archium.ateneo.edu/mathematics-faculty-pubs/236
https://doi.org/10.1142/s1793557123501437
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spelling ph-ateneo-arc.mathematics-faculty-pubs-12372024-02-19T04:36:24Z Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2 Manamtam, Jay R.A. Garciano, Agnes D. Tolentino, Mark Anthony C. Let G be a nontrivial connected graph and letc: V (G) → be a vertex coloring ofG, where adjacent vertices may have the same color. For a vertexv ofG, the color sumσ(v) ofv is the sum of the colors of the vertices adjacent tov. The coloringc is said to be a sigma coloring ofG ifσ(u)σ(v) wheneveru andv are adjacent vertices inG. The minimum number of colors that can be used in a sigma coloring ofG is called the sigma chromatic number ofG and is denoted byσ(G). In this study, we show that the sigma chromatic number of the middle graph of full binary trees of heighth is 2. We also determine a lower bound for the sigma chromatic number of graphs containing an induced subgraph isomorphic to a complete graph joined by pendant vertices. With this lower bound, we obtain the sigma chromatic number of the middle graph of the graphsGn,t,cor(Kn), stars, bistars, and the middle graph of some families of trees of height 2. 2023-08-01T07:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/236 https://doi.org/10.1142/s1793557123501437 Mathematics Faculty Publications Archīum Ateneo middle graph sigma chromatic number sigma coloring Vertex coloring 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 middle graph
sigma chromatic number
sigma coloring
Vertex coloring
Mathematics
Physical Sciences and Mathematics
spellingShingle middle graph
sigma chromatic number
sigma coloring
Vertex coloring
Mathematics
Physical Sciences and Mathematics
Manamtam, Jay R.A.
Garciano, Agnes D.
Tolentino, Mark Anthony C.
Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
description Let G be a nontrivial connected graph and letc: V (G) → be a vertex coloring ofG, where adjacent vertices may have the same color. For a vertexv ofG, the color sumσ(v) ofv is the sum of the colors of the vertices adjacent tov. The coloringc is said to be a sigma coloring ofG ifσ(u)σ(v) wheneveru andv are adjacent vertices inG. The minimum number of colors that can be used in a sigma coloring ofG is called the sigma chromatic number ofG and is denoted byσ(G). In this study, we show that the sigma chromatic number of the middle graph of full binary trees of heighth is 2. We also determine a lower bound for the sigma chromatic number of graphs containing an induced subgraph isomorphic to a complete graph joined by pendant vertices. With this lower bound, we obtain the sigma chromatic number of the middle graph of the graphsGn,t,cor(Kn), stars, bistars, and the middle graph of some families of trees of height 2.
format text
author Manamtam, Jay R.A.
Garciano, Agnes D.
Tolentino, Mark Anthony C.
author_facet Manamtam, Jay R.A.
Garciano, Agnes D.
Tolentino, Mark Anthony C.
author_sort Manamtam, Jay R.A.
title Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
title_short Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
title_full Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
title_fullStr Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
title_full_unstemmed Sigma Chromatic Number of the Middle Graph of Some General Families of Trees of Height 2
title_sort sigma chromatic number of the middle graph of some general families of trees of height 2
publisher Archīum Ateneo
publishDate 2023
url https://archium.ateneo.edu/mathematics-faculty-pubs/236
https://doi.org/10.1142/s1793557123501437
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