Chromatic Zagreb indices for graphical embodiment of colour clusters

International audienceFor a colour cluster C = (C 1 , C 2 , C 3 ,. .. , C), where C i is a colour class such that |C i | = r i , a positive integer, we investigate two types of simple connected graph structures G C 1 , G C 2 which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G C 1) = χ(G C 2) = and min{ε(G C 1)} = min{ε(G C 2)} = i=1 r i − 1, and ε(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G C 1 , G C 2

Notes on the Localization of Generalized Hexagonal Cellular Networks

The act of accessing the exact location, or position, of a node in a network is known as the localization of a network. In this methodology, the precise location of each node within a network can be made in the terms of certain chosen nodes in a subset. This subset is known as the locating set and its minimum cardinality is called the locating number of a network. The generalized hexagonal cellular network is a novel structure for the planning and analysis of a network. In this work, we considered conducting the localization of a generalized hexagonal cellular network. Moreover, we determined and proved the exact locating number for this network. Furthermore, in this technique, each node of a generalized hexagonal cellular network can be accessed uniquely. Lastly, we also discussed the generalized version of the locating set and locating number

Motor and Somatosensory Evoked Potential Monitoring Without Wakeup Test during Scoliosis Surgery

Background: Available evidence suggests that Transcranial electric motor evoked potentials and somatosensory evoked potential are safe methods to check the integrity of the spinal cord during spine deformity correction surgery. We compare the efficacy of Transcranial electric motor evoked potentials and somatosensory evoked potential to detect the nerve injury during Scoliosis surgery. Objectives: To demonstratethe advantages of combined motor and sensory evoked potential monitoring during Scoliosis surgery. Methods: We analyzed records of 65 (48 female and 17 male) Scoliosis surgery cases of Transcranial electric motor evoked potential and Somatosensory evoked potential.Mean age was 15.6 years. Patients who showed significant (at least 55%) of unilateral or bilateral amplitude loss , for at least five to ten minutes during the intervention in scoliosis surgery under total intravenous anesthesia will be included. Results: From 65 patients during surgery seventeen patients have a significant or complete drop of baseline amplitude on transcranial electric motor evoked potentials. Thirteen patients have the complete return of baseline amplitude by surgeon intraoperative intervention, whereas four patients havea reversal of motor response after 8 hours post-operatively. Transcranial electric motor evoked potential monitoring was 100% specific and 100% sensitive, whereas Somatosensory evoked potential was 100% specific and 85% sensitive. Conclusions: SSEPs and MEPs , in combination give accurate and quick information of nerve or spinal cord insult intraoperatively

Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Let $G=(V(G),E(G))$ be a molecular graph, where $V(G)$ and $E(G)$ are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity and the terminal Wiener indices are the distance based topological indices. In this paper, we described a linear time algorithm {\bf(LTA)} that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time $O(n)$

Hamltonian Connectedness and Toeplitz Graphs

A square matrix of order n is called Toeplitz matrix if it has constant elements along all diagonals parallel to the main diagonal and a graph is called Toeplitz graph if its adjacency matrix is Toeplitz. In this paper we proved that the Toeplitz graphs , for   and  are Hamiltonian  connected