The Descriptive Complexity of Subgraph Isomorphism Without Numerics
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DOI: 10.1007/s00224-018-9864-3
Abstract: Let F be a connected graph with ℓ vertices. The existence of a subgraph isomorphic to F can be defined in first-order logic with quantifier depth no better than ℓ, simply because no first-order formula… read more here.
Keywords: descriptive complexity; connected graphs; quantifier depth; subgraph ... See more keywords
On minimally 2-connected graphs with generalized connectivity $$\kappa _{3}=2$$κ3=2
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DOI: 10.1007/s10878-016-0075-z
Abstract: For $$S\subseteq G$$S⊆G, let $$\kappa (S)$$κ(S) denote the maximum number r of edge-disjoint trees $$T_1, T_2, \ldots , T_r$$T1,T2,…,Tr in G such that $$V(T_i)\cap V(T_j)=S$$V(Ti)∩V(Tj)=S for any $$i,j\in \{1,2,\ldots ,r\}$$i,j∈{1,2,…,r} and $$i\ne j$$i≠j. For every… read more here.
Keywords: graphs; connectivity; graphs generalized; kappa ... See more keywords
On the ABC index of connected graphs with given degree sequences
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DOI: 10.1007/s10910-017-0802-4
Abstract: The atom-bond connectivity (ABC) index of a graph G is defined to be $$ABC(G)=\sum _{uv\in E(G)}\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$$ABC(G)=∑uv∈E(G)d(u)+d(v)-2d(u)d(v) where d(u) is the degree of a vertex u. The ABC index plays a key role in correlating the… read more here.
Keywords: index; graphs given; given degree; index connected ... See more keywords
Minimal least eigenvalue of connected graphs of order n and size m = n + k (5 ⩽ k ⩽ 8)
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DOI: 10.1007/s11464-019-0805-5
Abstract: The least eigenvalue of a connected graph is the least eigenvalue of its adjacency matrix. We characterize the connected graphs of order n and size n + k (5 ⩽ k ⩽ 8 and n… read more here.
Keywords: least eigenvalue; eigenvalue connected; minimal least; graphs order ... See more keywords
On connected graphs of order n with girth g and nullity n − g
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DOI: 10.1016/j.laa.2021.07.005
Abstract: Abstract Let G be a simple graph of order n. The nullity of a graph G, denoted by η ( G ) , is the multiplicity of 0 as an eigenvalue of its adjacency matrix.… read more here.
Keywords: girth; cycle; connected graphs; nullity ... See more keywords
On the bounds of degree-based topological indices of the Cartesian product of F-sum of connected graphs
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DOI: 10.1186/s13660-017-1579-5
Abstract: Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and… read more here.
Keywords: topological indices; sum connected; index; cartesian product ... See more keywords