we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

Reactome is a free, open-source, open-data, curated and peer-reviewed knowledgebase of biomolecular pathways. One of its main priorities is to provide easy and efficient access to its high quality curated data. At present, biological pathway databases typically store their contents in relational databases. This limits access efficiency because there are performance issues associated with querie...

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graphmatrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris’ question...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

Resting state connectivity has been increasingly studied to investigate the effects of aging on the brain. A reduced organization in the communication between brain areas was demonstrated by combining a variety of different imaging technologies (fMRI, EEG, and MEG) and graph theory. In this paper, we propose a methodology to get new insights into resting state connectivity and its variations wi...

the prevalent communications networks suffer from lack of spectrum and spectrum inefficiency. this has motivated researchers to develop cognitive radio (cr) as a smart and dynamic radio access promised solution. a major challenge to this new technology is how to make fair assignment of available spectrum to unlicensed users, particularly for smart grids communication. this paper introduces an i...

ion of Graph Transformation Systems by Temporal Logic and Its Verification Mitsuharu Yamamoto, Yoshinori Tanabe, Koichi Takahashi, and Masami Hagiya 1 Faculty of Science, Chiba University 2 Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology (AIST) 3 Japan Science and Technology Agency 4 Graduate School of Information Science and Tech...

Although pictorial renditions of statistical data are ubiquitous, few techniques and standards exist to exchange, search and query these graphical representations. We present several improvements to human-graph interaction including i) a new approach to manage statistical graph knowledge by semantic annotation of graphs that bridges the gap between Web 2.0 social tagging and formal, logic-based...

For a graph G with m edges let its Range of Subgraph Sizes (RSS) ρ(G) = {t : G contains a vertex-induced subgraph with t edges}. G has a full RSS if ρ(G) = {0, 1, . . . ,m}. We establish the threshold for a random graph to have a full RSS and give tight bounds on the likely RSS of a dense random graph. ∗Current Address: School of Mathematics, Georgia Institute of Technology, Atlanta GA30332 †Su...