The normalized Laplacian makes a great contribution on analyzing the structure properties of nonregular graphs. Let O n be a linear octagonal-quadrilateral network.In this article, we first concern the normalized Laplacian spectrum of O n based on the decomposition theorem for the corresponding matrices. Then we derive the closed-term formulas of the degree-Kirchhoff index and the number of spanning trees of linear octagonal-quadrilateral networks on the basis of the relations between the roots and coefficients, respectively.
K E Y W O R D Sdegree-Kirchhoff index, normalized Laplacian, spanning tree
The Quark Matter 2006 conference was held on 14–20 November 2006 at the Shanghai Science Hall of the Shanghai Association of Sciences and Technology in Shanghai, China. It was the 19th International Conference on Ultra-Relativistic Nucleus–Nucleus Collisions. The conference was organized jointly by SINAP (Shanghai Institute of Applied Physics, Chinese Academy of Sciences (CAS)) and CCNU (Central China Normal University, Wuhan). Over 600 scientists from 32 countries in five continents attended the conference. This is the first time that China has hosted such a premier conference in the field of relativistic heavy-ion collisions, an important event for the Chinese high energy nuclear physics community. About one half of the conference participants are junior scientists—a clear indication of the vigor and momentum for this field, in search of the fundamental nature of the nuclear matter at extreme conditions.Professor T D Lee, honorary chair of the conference and one of the founders of the quark matter research, delivered an opening address with his profound and philosophical remarks on the recent discovery of the nature of strongly-interacting quark-gluon-plasma (sQGP). Professor Hongjie Xu, director of SINAP, gave a welcome address to all participants on behalf of the two hosting institutions. Dr Peiwen Ji, deputy director of the Mathematics and Physics Division of the Natural Science Foundation of China (NSFC), also addressed the conference participants and congratulated them on the opening of the conference. Professor Mianheng Jiang, vice president of the Chinese Academy of Sciences (CAS), gave a concise introduction about the CAS as the premier research institution in China. He highlighted continued efforts at CAS to foster international collaborations between China and other nations. The Quark Matter 2006 conference is an example of such a successful collaboration between high energy nuclear physicists in China and other nations all over the world.The scientific program of the conference began with an overview of high energy nuclear physics in China by Professor Wenqing Shen, vice president of the National Natural Science Foundation of China. Professor Shen highlighted many contributions made by the Chinese scientists in both theory and experiment. Dr Nick Samios, former director of Brookhaven National Laboratory (BNL), gave a vivid account of the early years of RHIC and recent accomplishments.Highlights of the conference include new results from RHIC at BNL and SPS (Super Proton Synchrotron) at CERN (European Organization for Nuclear Research). Many experimental results reported at the conference support the notion that the quark-gluon matter at RHIC behaves like a perfect liquid with minimum viscosity to entropy ratio. There were 15 plenary sessions which covered 54 plenary talks, 12 parallel sessions and 1 poster session. A total of 320 abstracts were submitted to the conference out of which 124 were selected for oral presentation and the rest were assigned to the poster session. Talks and posters in the co...
The general sum-connectivity index of a graph G is a molecular descriptor defined asdenotes the degree of vertex u in G and α is a real number. In this paper, we obtain the first third graphs with maximum general sum-connectivity index among the connected tricyclic graphs of order n for α ≥ 1 by four transformations which increase the general sum-connectivity index.
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