Full Edge-Friendly Index Sets of One Point Union of Cycles
Let G = (V, E) be a graph with vertex set V and edge set E. An edge labeling f : E → Z2 induces a vertex labeling f+ : V → Z2 defined by f+(v) ≡ P f(uv) (mod 2), for each vertex uv∈E v ∈ V. For i ∈ Z2, let vf(i) = |{v ∈ V: f+(v) = i}| and ef(i) = |{e ∈ E : f(e) = i}|. An edge labeling f of a graph G...
| Published in: | Ars Combinatoria |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Charles Babbage Research Centre
2024
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| Online Access: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85200372701&doi=10.61091%2fars159-03&partnerID=40&md5=c6db0b1dab801cd38f04bc9d9a9ca20e |
| Summary: | Let G = (V, E) be a graph with vertex set V and edge set E. An edge labeling f : E → Z2 induces a vertex labeling f+ : V → Z2 defined by f+(v) ≡ P f(uv) (mod 2), for each vertex uv∈E v ∈ V. For i ∈ Z2, let vf(i) = |{v ∈ V: f+(v) = i}| and ef(i) = |{e ∈ E : f(e) = i}|. An edge labeling f of a graph G is said to be edge-friendly if |ef(1) − ef(0)| ≤ 1. The set {vf(1) − vf(0): f is an edge-friendly labeling of G} is called the full edge-friendly index set of G. In this paper, we shall determine the full edge-friendly index sets of one point union of cycles. © 2024 the Author(s) |
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| ISSN: | 3817032 |
| DOI: | 10.61091/ars159-03 |