Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a signed graph, and the theory takes a par...

Recently three prime cordial labeling behavior of path, cycle, complete graph, wheel, comb, subdivison of a star, bistar, double comb, corona of tree with a vertex, crown, olive tree and other standard graphs were studied. Also four prime cordial labeling behavior of complete graph, book, flower were studied. In this paper, we investigate the four prime cordial labeling behavior of corona of wh...

A perfect path double cover (PPDC) of a graph G is a family P of paths of G such that every edge of G belongs to exactly two paths of P and each vertex of G occurs exactly twice as an endpoint of a path in P. Li (J. Graph Theory 14 (1990) 645–650) has shown that every simple graph has a PPDC.A regular perfect path double cover (RPPDC) of a graph G is a PPDC of G in which all paths are of the sa...

A connected graph is double connected if its complement is also connected The following Ramsey type theorem is proved in this paper There exists a function h n de ned on the set of integers exceeding three such that every double connected graph on at least h n vertices must contain as an induced subgraph a special double connected graph which is either one of the following graphs or the complem...

A connected graph is double-connected if its complement is also connected. The following Ramsey-type theorem is proved in this paper. There exists a function h(n), deened on the set of integers exceeding three, such that every double-connected graph on at least h(n) vertices must contain, as an induced subgraph, a special double-connected graph, which is either one of the following graphs or th...

We investigate some relations between a generic immersion of a graph into the 2-space with small number of double points and the embeddings of the graph into the 3-space obtained by lifting the immersion with respect to the natural projection from the 3-space to the 2-space. Specifically we prove: (1) An embedding of a graph obtained from a generic immersion of the graph with at most three doub...

A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect...

An irregularity index IR(Γ) of a graph Γ is nonnegative numeric quantity (i.e., IR(Γ)≥0) such that IR(Γ)=0 iff regular graph. In this paper, we show IRC closely correlates with the normal boiling point Tbp and standard heat formation ΔHfo lower benzenoid hydrocarbons. The correlation models fit data efficiently for both are linear. We develop further mathematical properties by calculating its e...

In a graph, a vertex is said to dominate itself and all its neighbors. A double dominating set of a graph G is a subset of vertices that dominates every vertex of G at least twice. The double domination number γ×2(G) is the minimum cardinality of a double dominating set of G. A graph G without isolated vertices is called edge removal critical with respect to double domination, or just γ×2-criti...