For a graph G a bijection from the vertex set and the edge set of G to the set {1, 2, . . . , |V (G)| + |E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total label...

Given an n-vertex graph G, an edge-coloring of G with natural numbers is a consecutive (or interval) coloring if the colors of edges incident with each vertex are distinct and form an interval of integers. In this paper we prove that if G has a consecutive coloring and n¿3 then S(G)62n − 4, where S(G) is the maximum number of colors allowing a consecutive coloring. Next, we investigate the so-c...

Z k-magic labelings of fans and wheels with magic-value zero Abstract Let A be a non-trivial abelian group and A * = A − {0}. A graph is A-magic if there exists an edge labeling using elements of A * which induces a constant vertex labeling of the graph. For fan graphs F n and wheel graphs W n , we determine the sets of numbers k ∈ N, where F n and W n have Z k-magic labelings with magic-value 0.

An exact formula for the expected length of the minimum spanning tree of a connected graph, with independent and identical edge distribution, is given, which generalizes Steele’s formula in the uniform case. For a complete graph, the difference of expected lengths between exponential distribution, with rate one, and uniform distribution on the interval (0, 1) is shown to be positive and of rate...

The geometric simultaneous embedding problem asks whether two planar graphs on the same set of vertices in the plane can be drawn using straight lines, such that each graph is plane. Geometric simultaneous embedding is a current topic in graph drawing and positive and negative results are known for various classes of graphs. So far only connected graphs have been considered. In this paper we pr...

To determine the (k, l)-radius of a graph we have to find a set L of l vertices, such that the maximum k-distance of a set K, where |K| = k and L ⊆ K, attains the minimum value in a graph. This notion generalizes the radius, diameter and k-diameter. In this contribution the (k, l)-radius of the wheel Wn is determined for all possible values of parameters k and l.

A simple random walk on a graph is defined in which a particle moves from one vertex to any adjacent vertex, each with equal probability. The expected hitting time is the expected number of steps to get from one vertex to another before returning to the starting vertex. In this paper, using the electrical network approach, we provide explicit formulae for expected hitting times for simple rando...

Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling, Magic labeling, Prime labeling, and other different labeling techniques.In this paper the Prime labeling of certain classes of graphs are discussed.It is of interest to note that H-graph which is a 3 –regular graph satisfy Prime labeling. A Gear graph is a graph obt...

Practical algorithms for solving the Subgraph Homeomorphism Problem are known for only a few small pattern graphs: among these are the wheel graphs with four, five, six, and seven spokes. The length and difficulty of the proofs leading to these algorithms increase greatly as the size of the pattern graph increases. Proving a result for the wheel with six spokes requires extensive case analysis ...

Intent detection and slot filling are recognized as two very important tasks in a spoken language understanding (SLU) system. In order to model these at the same time, many joint models based on deep neural networks have been proposed recently archived excellent results. addition, graph network has made good achievements field of vision. Therefore, we combine advantages propose new with wheel-g...