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DISTANCE-BASED SHADOW POLYNOMIAL OF THE JOIN OF GRAPHS AND ITS PROPERTIES
Keywords:
graph polynomial, Distance Distribution, Graph dynamicsDOI:
https://doi.org/10.17654/0972087126011Abstract
The notion of the k-distance shadow set, defined as the collection of vertices exactly k steps away from a given subset is the central idea to this study. For each fixed k, a partial shadow polynomial is formulated by summing over all shadow sets, and their collective sum yields the distance-based shadow polynomial. The paper establishes foundational properties of this polynomial and investigates its behavior under the join operation of two graphs. The construction captures how both neighborhood-level interactions and broader graph connectivity contribute to layered distance dynamics.
Received: July 1, 2025
Revised: July 13, 2025
Accepted: August 5, 2025
References
The notion of the k-distance shadow set, defined as the collection of vertices exactly k steps away from a given subset is the central idea to this study. For each fixed k, a partial shadow polynomial is formulated by summing over all shadow sets, and their collective sum yields the distance-based shadow polynomial. The paper establishes foundational properties of this polynomial and investigates its behavior under the join operation of two graphs. The construction captures how both neighborhood-level interactions and broader graph connectivity contribute to layered distance dynamics.
Received: July 1, 2025
Revised: July 13, 2025
Accepted: August 5, 2025
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