On twin edge colorings in m-ary trees

Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The...

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Main Authors: Tolentino, Jayson D, Marcelo, Reginaldo M, 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/217
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1218&context=mathematics-faculty-pubs
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spelling ph-ateneo-arc.mathematics-faculty-pubs-12182022-11-23T01:45:49Z On twin edge colorings in m-ary trees Tolentino, Jayson D Marcelo, Reginaldo M Tolentino, Mark Anthony C Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′t(G). In this paper, we study the twin edge colorings in m-ary trees for m ≥ 2; in particular, the twin chromatic indexes of full m-ary trees that are not stars, r-regular trees for even r ≥ 2, and generalized star graphs that are not paths nor stars are completely determined. Moreover, our results confirm the conjecture that χ′t(G)≤Δ(G)+2 for every connected graph G (except C5) of order at least 3, for all trees of order at least 3. 2022-01-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/217 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1218&context=mathematics-faculty-pubs Mathematics Faculty Publications Archīum Ateneo twin-edge coloring edge coloring vertex coloring m-ary trees 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 twin-edge coloring
edge coloring
vertex coloring
m-ary trees
Mathematics
Physical Sciences and Mathematics
spellingShingle twin-edge coloring
edge coloring
vertex coloring
m-ary trees
Mathematics
Physical Sciences and Mathematics
Tolentino, Jayson D
Marcelo, Reginaldo M
Tolentino, Mark Anthony C
On twin edge colorings in m-ary trees
description Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′t(G). In this paper, we study the twin edge colorings in m-ary trees for m ≥ 2; in particular, the twin chromatic indexes of full m-ary trees that are not stars, r-regular trees for even r ≥ 2, and generalized star graphs that are not paths nor stars are completely determined. Moreover, our results confirm the conjecture that χ′t(G)≤Δ(G)+2 for every connected graph G (except C5) of order at least 3, for all trees of order at least 3.
format text
author Tolentino, Jayson D
Marcelo, Reginaldo M
Tolentino, Mark Anthony C
author_facet Tolentino, Jayson D
Marcelo, Reginaldo M
Tolentino, Mark Anthony C
author_sort Tolentino, Jayson D
title On twin edge colorings in m-ary trees
title_short On twin edge colorings in m-ary trees
title_full On twin edge colorings in m-ary trees
title_fullStr On twin edge colorings in m-ary trees
title_full_unstemmed On twin edge colorings in m-ary trees
title_sort on twin edge colorings in m-ary trees
publisher Archīum Ateneo
publishDate 2022
url https://archium.ateneo.edu/mathematics-faculty-pubs/217
https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1218&context=mathematics-faculty-pubs
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