Author(s):
1. Waqar Ali:
University Malaysia Terengganu,
Abstract:
Let ?? = (??, ??) be a simple graph, where V denotes the set of vertices and ?? represents the set of edges. The first Zagreb index is defined by Z1(??) = ∑??∈??(??) = d(??)22, and the second Zagreb index is given as Z2(??) = ∑??∈??(??) = d(u)d(??). The metric dimension of a graph refers to the smallest possible size of a resolving set, which is a subset of vertices such that the distances from these vertices uniquely determine the position of every other vertex in the graph. In this paper, we investigate bounds for the Zagreb indices of trees with respect to their order and metric dimension. Moreover, we characterize the trees that attain these extremal bounds, offering new insights into how the metric dimension affects the behavior of the Zagreb indices in tree structures.
Page(s):
164-164
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
Zagreb indices
,
Metric dimension
References:
References are not available for this document.
Citations
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