Odd Harmonious Labeling on Edge Amalgamation from Double Quadrilateral Graphs

A graph that has odd harmonious labeling properties is called an odd harmonious graph. The purpose of this research is to obtain a new class graphs construction which is a family of odd harmonious graphs. The research method used consisted of several stages, namely research preparation, research investigation and verifivation of research results. The results of this study, we will give a line amalgamation construction of n double quadrilateral graphs DQ, denoted by *DQ(n) with n>= 1 and graph obtained by connecting between two graphs *DQ(n) with line graph L2, denoted by *(DQ(n),L2,DQ(n)). It has further been proven that *DQ(n) and *(DQ(n),L2,DQ(n)) have odd harmonious labeling properties, such that all of them are odd harmonious graphs.

A new spectrum of recursive models using an amalgamation construction

We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite language whose only recursively presentable model is saturated, gives the second non-trivial example of a spectrum produced in a finite language.