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On Pseudo-Balancing of Path-Induced Signed Graphs

Jomon Kottarathil

Department of Mathematics, St.Joseph’s College, Moolamattom Arakulam-685 591, Kerala, India

Email address:  jomoncmi@gmail.com

Doi : https://doi.org/10.47013/16.3.4

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 431 - 443

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Received on: June 7, 2022;                                         Accepted on: Nov. 22, 2022

 Abstract. The path decomposition of a graph G is the partition of its edges into distinct paths. Pendant number of a graph G is the least number of terminal vertices involved in the path decomposition of G. If the signed function is induced by the terminal vertices of the path-decomposed graph, it is called path-induced signed graph. In this paper, we identify few classes of balanced signed graphs and also introduce and examine a related concept, namely, pseudo-balancing of path-induced signed graphs.

Keywords: Path decomposition, pendant number, signed graphs, path-induced signed graphs, pseudo-balanced path-induced signed graphs.