Please use this identifier to cite or link to this item: https://ir.swu.ac.th/jspui/handle/123456789/12847
ชื่อเรื่อง: The unique γ-min labelings of graphs
ผู้แต่ง: Saduakdee S.
Khemmani V.
วันที่เผยแพร่: 2018
บทคัดย่อ: Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f: V (G) → {0, 1, 2, …, m} that induces an edge-labeling f′: E(G) → {1, 2, …, m} on G defined by f′ (e) = |f(u) − f(v)|, for each edge e = uv in E(G). The value of f is defined as val (Formula presented) The maximum value of a γ-labeling of G is defined as valmax(G) = max{val(f): f is a γ-labeling of G}; while the minimum value of a γ-labeling of G is valmin(G) = min{val(f): f is a γ-labeling of G}. A γ-labeling g of G is a γ-max labeling if val(g) = valmax(G) and a γ-labeling h is a γ-min labeling if val(h) = valmin(G). For a γ-labeling f of a graph G of size m, the complementary labeling (Formula presented) of f is defined by (Formula presented). Let G be a connected graph and f a γ-min labeling of G. Then G has a unique γ-min labeling if f and (Formula presented) are only two γ-min labelings of G. In this paper, we study a connected graph having the unique γ-min labeling. The minimum value of a γ-labeling is determined for some classes of trees. Spontaneously, we are able to find that they have no unique γ-min labeling. © 2018 by the Mathematical Association of Thailand. All rights reserved.
URI: https://ir.swu.ac.th/jspui/handle/123456789/12847
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85045005207&partnerID=40&md5=74cbb00dba8c9ec7f699af32abc944af
ISSN: 16860209
Appears in Collections:Scopus 1983-2021

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