We examine the simultaneous embedding with fixed edges problem for two planar graphs G1 and G2 with the focus on their intersection S = G1∩G2. In particular, we will present the complete set of intersection graphs S that guarantee a simultaneous embedding with fixed edges for (G1, G2). More formally, we define the subset ISEFE of all planar graphs as follows: A graph S lies in ISEFE if every pa...

We prove that the unique decomposition of connected graphs defined by Tutte is definable by formulas of Monadic Second-Order Logic. This decomposition has two levels: every connected graph is a tree of "2-connected components" called blocks ; every 2-connected graph is a tree of so-called 3-blocks. Our proof uses 2dags which are certain acyclic orientations of the considered graphs. We obtain a...

The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...

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In this paper, the vibration of microbeams due to a temperature pulse has been investigated. The thermoelastic coupled equations for microbeam resonator have been derived via the modified theory of couple stress in connection with the generalized thermoelasticity with relaxation time. The analytical expressions for studied fields due to modified couple stress for the microbeam have been obtaine...

This work defines the concepts of strong efficient dominating set and intuitionistic fuzzy graph. We also introduce an graph a number graphs. The dominant in graphs has some limitations that are studied, derived..

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...