International Journal For Multidisciplinary Research

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Sum Cordial Labeling of Banana Tree Graphs: Existence and Constructions

Author(s) Dr. Dibya Gulab Minj, Dr. Chiranjilal Kujur
Country India
Abstract Sum cordial labeling is a variation of cordial labeling in which a binary vertex labeling f:V(G)→{0,1} induces an edge labeling defined by f∗(uv)=f(u)+f(v)(mod2). A graph G is Sum cordial if ∣vf(0)−vf(1)∣≤1 and ∣ef(0)−ef(1)∣≤1, where vf(i) and ef(i) denote the number of vertices and edges labeled with i, respectively. This concept has been studied for various graph families due to its applications in network addressing and coding theory.
A banana tree Bm,n is a tree obtained by connecting one leaf from each of n copies of the star graph to a single new root vertex. Banana trees are of interest because of their symmetry and recursive structure, making them natural candidates for labeling problems. In this paper, we investigate the sum cordiality of banana trees. We establish necessary and sufficient conditions for a banana tree Bm,n to be Sum cordial in terms of the parameters m and n. Explicit algorithms for constructing Sum cordial labeling are presented when such labeling exist.
The proofs employ combinatorial counting techniques and parity arguments on the distribution of vertex and edge labels. This work extends previous results on cordial labeling of trees and provides a complete characterization of Sum cordial banana trees. The methods used here may be applied to other classes of trees formed by amalgamation of stars.
Keywords Sum cordial labeling, Banana tree, Graph labeling, Cordial graph, Tree amalgamation, Binary labeling
Field Computer > Data / Information
Published In Volume 8, Issue 3, May-June 2026
Published On 2026-06-01
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E-ISSN 2582-2160
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