Abstract. Operating only by means of the incidence matrix of a connected graph G, a new algebraic combinatorial method for determining the paths of length (q−1) of G together with the generators of the corresponding generalized graph ideal Iq(G) is discussed and developed. The stated formulae are obtained and shown even by changing techniques appropriately when the difficulties of calculation increased.

MSC: 05B20, 05C38, 05C50

Keywords: Combinatorics, incidence matrices, paths, graph ideals.

DOI 10.56082/annalsarscimath.2024.1.57

Abstract Article Volume 16 no 1 / 2024

*Accepted for publication on August 8-th, 2023

[1] maurizio.imbesi@unime.it Address Department of Mathematical and Computer Sciences, Physical and Earth Sciences, University of Messina, Italy. The research that led to the paper was partially supported by a grant of the group GNSAGA of INdAM, Italy

[2] monica.labarbiera@unict.it Address Department of Electrical, Electronic and Computer Engineering, University of Catania, Italy