Abstract
In this study, we propose a new kind of graph labeling which we call logic labeling and investigate the logically labeling of the corona between paths P n and cycles C n , namely, P n ⊙ C m . A graph is said to be logical labeling if it has a 0 − 1 labeling that satisfies certain properties. The corona G 1 ⊙ G 2 of two graphs G 1 (with n 1 vertices and m 1 edges) and G 2 (with n 2 vertices and m 2 edges) is defined as the graph formed by taking one copy of G 1 and n 1 copies of G 2 and then connecting the i th vertex of G 1 with an edge to every vertex in the i th copy of G 2 .
Highlights
Graphs can be used to model a wide range of relationships and processes in physical, biological, social, and information systems
We show that Pn ⊙ Cm logical labeling if and only if (n, m) ≠ (1, 3(mod4))
We show that Pn ⊙ Cm is logical labeling if and only if (n, m) ≠ (1, 3(mod4))
Summary
Graphs can be used to model a wide range of relationships and processes in physical, biological, social, and information systems. Labeling methods are used for a wide range of applications in different subjects including coding theory, computer science, and communication networks. Graph labeling is an assignment of positive integers on vertices or edges or both of them which fulfilled certain conditions. Graceful labeling and harmonious labeling are two of the major styles of labeling. Graceful labeling is one of the most well-known graph labeling approaches; it was independently developed by Rosa in 1966 [3] and Golomb in 1972 [5], whilst harmonious labeling was initially investigated by Graham and Sloane in 1980 [6]. According to the definition of the corona, G1 ⊙ G2 has n1 + n1n2 vertices and m1 + n1m2 + n1n2 edges. We show that Pn ⊙ Cm logical labeling if and only if (n, m) ≠ (1, 3(mod4))
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