The circular consecutive choosability chcc(G) of a graph G has been recently introduced in [2]. In this paper we prove upper bounds on chcc for series-parallel graphs, planar graphs and k-choosable graphs. Our bounds are tight for classes of series-parallel graphs and k-choosable graphs for k ≥ 3. Then we study the circular consecutive choosability of generalized theta graphs. Lower bounds for ...

In this paper the definition of Location-2-Domination and minimum cardinality of Location-2-Domination are introduced and denoted by R D(G), and a theorem to find Location-2-dominating set for Path, cycle, Theta graph and Trees in different Kinds are introduced. AMS subject classification: 05C69.

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

A differential-difference operator is used to model the heat equation on a finite graph analogue of Poincaré’s upper half-plane. Finite analogues classical theta functions are shown be solutions in this setting.

By an ortho-radial drawing of a graph we mean a planar drawing on concentric circles such that each edge is an alternating sequence of circular and radial segments, where a circular segment is a part of a circle and a radial segment is a part of a half-line starting at the center of the circles. Ortho-radial drawings are topologically an extension of orthogonal drawings to drawings on a cylinde...

Recently the author introduced a semidefinite upper bound on the square of the stability number of a graph, the inverse theta number, which is proved here to be multiplicative with respect to the strong graph product, hence to be an upper bound for the square of the Shannon capacity of the graph. We also describe a heuristic algorithm for the stable set problem based on semidefinite programming...

We investigated the development of the brain's functional connectivity throughout the life span (ages 5 through 71 years) by measuring EEG activity in a large population-based sample. Connectivity was established with Synchronization Likelihood. Relative randomness of the connectivity patterns was established with Watts and Strogatz' (1998) graph parameters C (local clustering) and L (global pa...

We define non-commutative versions of the vertex packing polytope, theta convex body and fractional polytope a graph, establish quantum version Sandwich Theorem Grötschel, Lovász Schrijver (1986) [7]. new number graph which lead to an upper bound zero-error capacity corresponding channel that can be genuinely better than one established by Duan, Severini Winter (2013) [5]. counterparts widely u...

Augmented Lazy Theta*: Applying Graph Abstractions to Trajectory Planning with Speed-Limit Constraints Peter Gregory Digital Futures Institute School of Computing Teesside University, UK [email protected] Lukáš Chrpa PARK research group School of Computing and Engineering University of Huddersfield, UK

In this paper, we focus on solving the decentralized optimization problem of minimizing sum n objective functions over a multi-agent network. The agents are embedded in an undirected graph where they can only send/receive information directly to/from their immediate neighbors. Assuming smooth and strongly convex functions, propose Optimal Gradient Tracking (OGT) method that achieves optimal gra...