
TL;DR
This paper introduces the concept of $k$-geometric mean graphs, explores new classes of such graphs, and investigates their properties and labelings, extending the existing theory of geometric mean graphs.
Contribution
It defines $k$-geometric mean labeling, proves certain classes of graphs are $k$-geometric mean graphs, and studies join operations preserving geometric mean labelings.
Findings
Identified new classes of $k$-geometric mean graphs.
Proved some graph classes admit $k$-geometric mean labelings.
Analyzed join operations maintaining geometric mean labelings.
Abstract
A finite, simple and undirected graph with vertices and edges is said to be a -geometric mean graph for a positive integer if there is an injection such that, when each edge is assigned the label or , the resulting edge label set is and is called a \emph{-geometric mean labeling} of . The special case , a -geometric mean labeling is called a geometric mean labeling, and a -geometric mean graph is called a geometric mean graph. In this paper, we present new classes of geometric mean graphs. Then we introduce -geometric mean labeling and prove some classes of graphs are -geometric mean. We also study some classes of finite join of graphs that admit geometric mean labeling.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems
