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A sequence which is the degree sequence of some simple graph, i.e. for which the degree sequence problem has a solution, is called a graphic or graphical sequence. As a consequence of the degree sum formula, any sequence with an odd sum, such as (3, 3, 1), cannot be realized as the degree sequence of a graph. The inverse is also true: if a ...
Originally the second of three degrees in sequence – Legum Baccalaureus (LL.B., last conferred by an American law school in 1970); LL.M.; and Legum Doctor (LL.D.) or Doctor of Laws, which has only been conferred in the United States as an honorary degree but is an earned degree in other countries. In American legal academia, the LL.M. was ...
A degree is any of a wide range of status levels conferred by institutions of higher education, such as universities, normally as the result of successfully completing a program of study. Academic dress (or academical dress, also known in the United States as academic regalia) Traditional clothing worn specifically in academic settings.
[1] The definition of education has been explored by theorists from various fields. [2] Many agree that education is a purposeful activity aimed at achieving goals like the transmission of knowledge, skills, and character traits. [3] However, extensive debate surrounds its precise nature beyond these general features.
Although credit transfer can be conducted between education bodies in separate countries, the process of articulation can become very complicated when students transfer courses earned at multiple and international campuses, transfer courses from more than 5–10 years ago, or have alternative credit experiences such as exam or military credit.
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics.It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
It exactly preserves the degree sequence of a given graph by assigning stubs (half-edges) to nodes based on their degrees and then randomly pairing the stubs to form edges. The preservation of the degree sequence is exact in the sense that all realizations of the model result in graphs with the same predefined degree distribution.
Let the degree sequence of a graph G be d 1 ≥ d 2 ≥ … ≥ d n, and let m be the largest value of i such that d i ≥ i – 1. Then G is a split graph if and only if = = + = +. If this is the case, then the m vertices with the largest degrees form a maximum clique in G, and the remaining vertices constitute an independent set. [13]