کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598471 1631089 2016 57 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Beyond graph energy: Norms of graphs and matrices
ترجمه فارسی عنوان
فراتر از انرژی گراف: مقادیر نمودار و ماتریس
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In 1978 Gutman introduced the energy of a graph as the sum of the absolute values of graph eigenvalues, and ever since then graph energy has been intensively studied.Since graph energy is the trace norm of the adjacency matrix, matrix norms provide a natural background for its study. Thus, this paper surveys research on matrix norms that aims to expand and advance the study of graph energy.The focus is exclusively on the Ky Fan and the Schatten norms, both generalizing and enriching the trace norm. As it turns out, the study of extremal properties of these norms leads to numerous analytic problems with deep roots in combinatorics.The survey brings to the fore the exceptional role of Hadamard matrices, conference matrices, and conference graphs in matrix norms. In addition, a vast new matrix class is studied, a relaxation of symmetric Hadamard matrices.The survey presents solutions to just a fraction of a larger body of similar problems bonding analysis to combinatorics. Thus, open problems and questions are raised to outline topics for further investigation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 506, 1 October 2016, Pages 82–138
نویسندگان
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