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October 9, 2025Open Access

On Sum Cordialness of Some Fractal Graph

Key Points

The research establishes that multiple types of fractal graphs can have a sum cordial labeling, enhancing our understanding of graph properties.
Notably, the Vicsek fractal, Box fractal, and Ladder Fractal Graphs of Type 1 to Type 4 all exhibit this unique labeling.
The definition of sum cordial labeling is vital for understanding the conditions that enable a graph to be categorized as sum cordial.
Sum cordial labeling involves strict conditions on vertex and edge counts, ensuring balance within the graph structure.

Abstract

For a graph G with vertex set V is a function f: V (G) →0. 1 with induced edge labeling such that f#: E (G) →0, 1 such that f# (pq) = (f (p) + f (q) ) (mod 2) for all pq \ (\) E (G) is called a sum cordial labeling, If |v (0) - v (1) |\ (\) 1 and |e (0) - e (1) |\ (\) 1. A graph that follows sum cordial labeling is called a sum cordial graph. We have proved that Vicsek fractal, Box fractal, Ladder Fractal Graph of Type – 1 to Type – 4 admits sum cordial labeling.

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Cite This Study

Khiraiya et al. (Wed,) studied this question.

synapsesocial.com/papers/68e7d631bd66d359be6268e9 https://doi.org/https://doi.org/10.9734/arjom/2025/v21i10994

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