IHARINA ZETA FUNKCIJA ZA KOMPLETNE GRAFOVE I NJIHOVU KOMBINACIJU
IHARA ZETA FUNCTION OF COMPLETE GRAPHS AND THEIR COMBINATIONS

Summary/Abstract: In this paper we investigate the application of Ihara zeta function to complete graphs and to graphs formed by the extended union of two complete graphs. Ihara zeta function serves as a tool for analyzing the cycle structures of graphs, providing insight into cycles of different lengths within graphs. The goal is to calculate Ihara zeta functions for complete graphs and for graphs obtained by combining two such graphs, and to examine how structural information from individual graphs is reflected in the zeta function of a more complex graph. Our analysis shows that the number of cycles of length 3, 4 and 5 in more complex graphs grows according to the rules that depend on the length of the cycle and the number of graph nodes, which confirms the possibility of predicting the growth of the number of cycles based on these coefficients.

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