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The strong edge-coloring of a graph G is a proper edge coloring such that all edges adjacent to any given edge receive different colors. Such an assignment of colors defines color classes all of which are induced matchings. The minimum number of color classes required for such an assignment of colors is defined as the strong chromatic index of a graph G. In this article, we discuss the strong chromatic index of graphs obtained by the amalgamation of two graphs, the rooted product of two graphs and the corona product of two graphs. [ABSTRACT FROM AUTHOR]

Let be a simple connected graph consisting of n vertices and m edges. In a proper l -coloring, an r -dynamic coloring of a graph is one in which each vertex's neighbors are provided at least min { r , d (k) } different colors. The r -dynamic chromatic number of graph , given as χ r () , is the minimal l such that the graph has r -dynamic l coloring of . In this study, we combine a few common graphs to provide the r -dynamic coloring of the subdivision-edge neighborhood corona of path graph P s and star graph K 1 , s . These graphs include path graph P q , cycle graph C q , complete graph K q , star graph K 1 , q , and double star graph K 1 , q , q . [ABSTRACT FROM AUTHOR]

Chen et al. [On coupon coloring of graphs, Discrete Appl. Math. 193 (2015) 94–101] had introduced the concept of coupon coloring for any graph with no isolated vertex. A k -coupon coloring of G is an assignment of colors from [ k ] : = { 1 , 2 , ... , k } to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [ k ]. The maximum k for which a k -coupon coloring exists is called the coupon coloring number of G , and is denoted by χ c (G). In this paper, we determine the coupon coloring number of Kneser graphs K (n , 2). [ABSTRACT FROM AUTHOR]

An injective k -edge coloring of a graph G is a k -edge coloring φ of G such that φ (e 1) ≠ φ (e 3) for any three consecutive edges e 1 , e 2 and e 3 of a path or a 3-cycle. The injective edge chromatic index of G , denoted by χ i ′ (G) , is the minimum k such that G has an injective k -edge coloring. Li and Chen determined the injective edge chromatic index of the generalized Petersen graph P (n , k) for 1 ≤ k ≤ 2. In this paper, we consider the injective edge coloring of the generalized Petersen graph P (c k , k) and show that χ i ′ (P (c k , k)) ≤ 5 for k ≥ 3. [ABSTRACT FROM AUTHOR]