Videolaringostroboscopy (VLS) is a first choice examination for diagnosis of several laryngeal pathologies. However, in case of strong a-periodicity of the vocal sound, it becomes ineffective in describing subsequent phases of the vocal cycle. To overcome such limitation, a new technique, named videokymography (VKG) has been developed. VKG delivers images from a single line selected from the wh...

the edge szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph g, where mu(e) is the number of edges which its distance to vertex u is smaller than the distance to vertex v, and nv(e) is defined analogously. in this paper, the edge szeged index of one-pentagonal carbon nanocone cnc5[n] is computed for the first ...

Let G[H] be the lexicographic product of graphs G and H and let G⊕H be their Cartesian sum. It is proved that if G is a nonbipartite graph, then for any graph H, χ(G[H]) ≥ 2χ(H)+d k e, where 2k+1 is the length of a shortest odd cycle of G. Chromatic numbers of the Cartesian sum of graphs are also considered. It is shown in particular that for χ–critical and not complete graphs G and H, χ(G ⊕ H)...

In this paper we explore structural properties of unitary Cayley graphs, including clique and chromatic number, vertex and edge connectivity, planarity, and crossing number.

An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). In this paper, we prove that every planar graph G admits an acyclic edg...

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let Q be an additive hereditary property of graphs. A Q-edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property Q. In this paper we present some results on fractional Q-edge-colorings. We determine...

An acyclic edge colouring of a graph is a proper edge colouring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge colouring using k colours and it is denoted by a′(G). Here, we obtain tight estimates on a′(G) for nontrivial subclasses of the family of 2-degenerate graphs. Specifically, we obtain values of...

We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost c...

We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for significance, and also those edge-signed graphs whose double covering graph is bipartite. If the property of even length is generalized to positivity in a second edge signing, the characterizations generalize as well. We also char...

It was conjectured in [S. Akbari, F. Khaghanpoor, and S. Moazzeni. Colorful paths in vertex coloring of graphs. Preprint] that, if G is a connected graph distinct from C7, then there is a χ(G)-coloring of G in which every vertex v ∈ V (G) is an initial vertex of a path P with χ(G) vertices whose colors are different. In [S. Akbari, V. Liaghat, and A. Nikzad. Colorful paths in vertex coloring of...