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G = (V(G),E(G)) be a simple undirected graph of order n and size m, and x, y, z be three variables taking value + or -. The transformation graph CzY- ......

Linear k-arboricity of complete bipartite graphs

A linear k-forest refers to a forest in which every component is a path of length at most k. The linear k-arboricity of a graph G is defined as the le......

A sufficient condition for fractional ID-[a, b]-factor-critical covered graphs

A graph G is fractional ID-[a, b]-factor-critical covered if for any independent set I of G, G I is fractional [a, b]-covered. In this article, we pre......

The intersection problem for S(2, 4, v)s with a common parallel class

A parallel class in a design is a set of blocks that partition the point set. The intersection problem for Steiner systems with a common parallel clas......

2-(v, k, 1) designs admitting automorphism groups with socle F-2(4)(q)

It is a large and demanding project for determining pairs (D, G) in which D is a 2 - (v, k, 1) design and G is a block-transitive group of automorphis......

Decycling d-ary n-dimensional Cubes

The decycling number of a graph G is the minimum number of vertices whose removal from G results in an acyclic subgraph. The d-ary n-dimensional cubes......

Isolated toughness and P->= 3-factors in graphs

Let m, n, k be three positive integers. A path factor with each component having at least n vertices is called a P >= n-factor. A graph G is define......

SOME EXTREMAL GRAPHS WITH RESPECT TO THE ZEROTH-ORDER GENERAL RANDIC INDEX

For a given graph set g(n), it is important to find the upper and lower bounds for some graph invariant in g(n) and characterize the graphs in which t......

Extremal unicyclic graphs with respect to the reformulated reciprocal product-degree distance

The reformulated reciprocal product-degree distance of a connected graph G is defined as RDDxt = RDDxt (G) = Sigma({u,v}subset of V(G) u not equal v) ......

On the spectral radius of bipartite graphs

The adjacency matrix A(G) of a graph G is the n x n matrix with its (i, j)-entry equal to 1 if u(i) and u(j) are adjacent, and 0 otherwise. The spectr......

On ID-Hamiltonian [a, b]-factor

Let a, b be two integers with 2 <= a < b. An [a, b]-factor F of a graph G is called a Hamiltonian [a, b]-factor if F includes a Hamiltonian cycl......

The expected values of Hosoya index and Merrifield-Simmons index in a random spiro chain

The Hosoya index m(G) and the Merrifield-Simmons index i(G) of a graph G are the number of matchings and the number of independent sets in G, respecti......

MULTIDIMENSIONAL GENERALIZATIONS OF THE RAMANUJAN'S FORMULAS

In this paper, by using probability versions of the Ramanujan's formulas, we obtain two multidimensional generalizations of Ramanujan's formulas for B......

A note on symmetric graphs of valency eight

A graph, with a group G of its automorphisms, is said to be (G, s)-transitive, if G is transitive on s-arcs but not on (s + 1)-arcs of the graph. Let ......

Magic squares with all subsquares of possible orders based on extended Langford sequences

A magic square of order n with all subsquares of possible orders (ASMS(n)) is a magic square which contains a general magic square of each order k is ......