Based on the researcher’s observation to students of mathematics education department ofUNIPA Surabaya, the material of graph theory taught in mathematics discrete course was adifficult course to be understood by the students coherently and deeply. To acknowledge the reasonthat caused the material of graph theory difficult to understand and to improve result of learningmathematics, was needed to conduct error analysis. The analyzed error covering the area and thetype as well as error-causing factor, was done by the students to complete graphic theory question.After recognizing the position and kind of error as well as the causing factor which was conductedby the students in completing the question of graph theory, we can determined its alternativesolution. The research type done by the researcher was descriptive. The research was done inUNIPA Surabaya. The core instrument in this research was the researcher itself, as the researcherwho planned, arranged, conducted, collected data, analyzes data, concluded and made theresearch report. The other instruments in this research were diagnostic test and interview manual.In this research, the data analysis technique was done through three stages, they are : datareduction, data presentation and conclusion. The error area done by the students of UNIPASurabaya of academic year 2010 to complete the problem of graph theory was in problem ofunderstanding, namely the inability to correlate the relation between information and problemsolving which has many misconception. The kinds of error done by the students of UNIPASurabaya of academic year 2010 to solve the graph theory were kind of principle error because itrelated to the error of understanding and implementing theorem as well as definition. The errorcausingfactors done by the students of UNIPA Surabaya of academic year 2010 to solve theproblem of graph theory generally was the lack of accuracy and not having the understanding oftheorems and definition to solve a problem. Based on the area, kinds, and factor caused the errorwhich was done by the students of UNIPA Surabaya of academic year 2010 to solve the problem ofgraph theory so that the alternative model of learning in which the researcher proposes is themodel of meta-cognitive learning.