Mohammad Hassan Shirdareh Haghighi

Mohammad Hassan Shirdareh Haghighi
Shiraz University · Department of Mathematics

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7
Publications
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Publications

Publications (7)
Article
A graph G of order 2n is called equipartite if for every n-element set A⊆V(G), there exists an automorphism of G that maps the induced subgraph G[A] onto G[V(G)∖A]. In this paper, we show that a graph G of order 2n is equipartite if and only if for every such partition of V(G), the induced subgraphs G[A] and G[V(G)∖A] have the same Laplacian spectr...
Article
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The Erdos-Gyárfás conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erdos-Gyárfás conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular for cubic claw-free grap...
Article
We generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
Article
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The Erd\H{o}s-Gy\'{a}rf\'{a}s conjecture states that every graph with minimum degree at least three has a cycle whose length is a power of 2. Since this conjecture has proven to be far from reach, Hobbs asked if the Erd\H{o}s-Gy\'{a}rf\'{a}s conjecture holds in claw-free graphs. In this paper, we obtain some results on this question, in particular...
Article
A graph $G$ of order $2n$ is called degree-equipartite if for every $n$-element set $A\subseteq V(G)$, the degree sequences of the induced subgraphs $G[A]$ and $G[V(G)\setminus A]$ are the same. In this paper, we characterize all degree-equipartite graphs. This answers Problem 1 in the paper by Gr\"{u}nbaum et al [B. Gr\"{u}nbaum, T. Kaiser, D. Kr\...
Article
We associate a graph Γ+(R) to a ring R whose vertices are nonzero proper right ideals of R and two vertices I and J are adjacent if I+J=R. Then we try to translate properties of this graph into algebraic properties of R and vice versa. For example, we characterize rings R for which Γ+(R) respectively is connected, complete, planar, complemented or...
Article
In this paper, we find recursive relations t(Ln) = 4t(Ln-1)-t(Ln-2), t(Fn) = 3t(Fn-1) - t(Fn-2), and t(Wn) = t(Wn-1) + t(Fn) + t(Fn-1), for determining the number of spanning trees in ladders Ln, fans Fn, and wheels Wn.