The cyclic ladder graph CLn is the Cartesian product of cycles Cn and paths P2, that CLn=Cn×P2, (n≥3). di-forcing polynomial a binary enumerative all perfect matching forcing anti-forcing numbers. In this paper, we derive recursive formulas for by classifying counting cases associated edges given vertex, from which obtain number matching, polynomials, generating function computing some polynomi...

A ladder lottery, known as the “Amidakuji” in Japan, is a common way to choose an assignment randomly. Formally, a ladder lottery of a permutation π = (p1, p2, . . . , pn) is a network with n vertical lines (lines for short) and many horizontal lines (bars for short) as follows (see Fig. 1). The i-th line from the left is called line i. The top ends of the n lines correspond to π. The bottom en...

A Ringel ladder can be formed by a self-bar-amalgamation operation on a symmetric ladder, that is, by joining the root vertices on its end-rungs. The present authors have previously derived criteria under which linear chains of copies of one or more graphs have log-concave genus polynomials. Herein we establish Ringel ladders as the first significant non-linear infinite family of graphs known t...

If two rays P,Q ⊂ G satisfy (i)–(iii), we call them end-equivalent in G. An end of G is an equivalence class under this relation, and E(G) denotes the set of ends of G. For example, the 2-way infinite ladder has two ends, the infinite grid Z×Z and every infinite complete graph have one end, and the dyadic tree has 20 ends. This paper is concerned with the relationship between the ends of a conn...

Antimagic labeling of a graph with vertices and edges is assigned the labels for its by some integers from set , such that no two received same label, weights are pairwise distinct. Where vertex-weights vertex under this sum all incident to vertex, in paper, we deal problem finding antimagic edge special families graphs called strong face graphs. We prove antimagic, ladder wheel fan prism final...

The Philosophers' Process is a Markovian version of the famous Dining Philosophers Problem introduced by Dijkstra as a model for resource sharing. It can be viewed as a reversible interacting particle system. This paper deals with the problem of computing its reversible measure in the case of a large but nite number of sites. This equilibrium measure is a Markov eld on the underlying graph of i...

The height of a trace is the height of the corresponding heap of pieces in Viennot’s representation, or equivalently the number of factors in its Cartier-Foata decomposition. Let h(t) and |t| stand respectively for the height and the length of a trace t. We prove that the bivariate commutative series ∑ t xy is rational, and we give a finite representation of it. We use the rationality to obtain...

LIPN, UMR CNRS 7030. Institut Galilée Université Paris-Nord, 99, avenue Jean-Baptiste Clément 93430 Villetaneuse, France. 2 Université Pierre et Marie Curie, Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600 Tour 16, 2 étage, 4, place Jussieu, F 75252 Paris Cedex 05, France. 3 H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences Division of Theoreti...

The prime index graph π(G) of a finite group G is special type undirected simple whose vertex set subgroups G, in which two distinct vertices are adjacent if one has the other. Let p and q be primes. In this paper, we establish that cyclic p-group Zpn, abelian Zpn × Zq Zp always have graceful labeling without any condition on n using concept path or p-layer ladder size + 1.

The height of a trace is the height of the corresponding heap of pieces in Viennot’s representation, or equivalently the number of factors in its Cartier-Foata decomposition. Let h(t) and |t| stand respectively for the height and the length of a trace t. We prove that the bivariate commutative series ∑ t xy is rational, and we give a finite representation of it. We use the rationality to obtain...