Work

Formulas for the Number of Weak Homomorphisms from Paths to Rectangular Grid Graphs

Year: 2025

Type: article

Abstract: A weak homomorphism from graph G to graph H is a mapping f:V(G)→V(H), where either f(x)=f(y) or {f(x),f(y)}∈E(H) hold for all {x,y}∈E(G). A rectangular grid graph is formed by taking the Cartesian product of two paths. Counting weak homomorphisms is a fundamental problem in graph theory. In this paper, we present formulas for calculating the number of weak homomorphisms from paths to rectangular grid graphs. This count directly corresponds to the number of partial walks with length m within the rectangular grid graph, offering a combinatorial solution to this enumeration problem.

Source: Symmetry

DOI: 10.3390/sym17040497

Authors: Penying Rochanakul, Hatairat Yingtaweesittikul, Sayan Panma

Institution: Chiang Mai University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: Chiang Mai University, Faculty of Science, Chiang Mai University